The only real support for fans who regard the Black Rose Saga as a filler arc, so I'm going to limit myself to noting [in response to Mark commenting that, had he watched this series in high school, he might have avoided some toxic relationships] that alas, Mark, I'm not sure watching this would have helped. I DID watch this show in high school, when it was new, and I was still all Nice Guy Syndrome until my mid-twenties.
Mikage's chalkboard when Akio visits him in the flashback is interesting. For a big scientific research project, it contains very little math. It does have what look like I Ching hexagrams and an inverted symbol of Venus/feminine/copper. Something to do with the Eternal Feminine, maybe?
As several people have noted, time is SERIOUSLY broken at Ohtori, possibly as a result of the project Nemuro was working on. Clothing styles have gone from 70s to 90s, and Tokiko has aged from maybe early 20s to maybe 40, but Mikage and Akio haven't aged a day. Neither has Mamiya, but either his death was faked or he's undead. Meanwhile, there's hints of time going faster than it should (the tea, the cats reproducing in the course of a conversation), slower (the stopped hourglass, the teacup still being there), and even backwards (the butterfly becoming an egg on a leaf).
Meanwhile, we see the duelists planting trees, and their sacrifice is so that one day the path to eternity can be opened from the school. Saionji stated that the upside-down castle is the place where eternity can be found; the implication would seem to be that the goal of the project was to create the dueling forest and arena.
The Shadow Girl play seems to be about Mikage, an apparently unfeeling robot. But note, it says it never gets lonely because it has the monkeys for company--that lack of feeling is just Mikage denying his emotions and therefore being controlled by them. (Hi there, Spock!) The monkeys he catches are, of course, the Black Rose duelists. The implication, then, is that his nefarious scheming is a doomed attempt to cope with his loneliness.
Of course, there's another way to read the play: Who else do we know that hides (from) their true feelings, pretends to have no will of their own, and has a monkey for a friend?
Oh, and I forgot: on the time is broken thing? That's the common fan theory on why Miki is always fiddling with the watch. He's noticed, and is trying to catch time in the act, so to speak. Note also that he's the first character to know anything about Nemuro Hall--I suspect he's figured out its somehow connected to the time distortions.
Best duel song of the arc, IMO. Weirdly straightforward Shadow Girl play, too: it's pretty clearly about how pathetic it is to cling to past accomplishments instead of moving forward into the future and forging new ones.
Mikage/Nemuro's goal, we learn, was to make his memories eternal. I'm guessing what happened was, roughly, that they opened the path to eternity just too late to save Mamiya, and Nemuro burned the place down in rage and grief, or possibly as part of a bargain with Akio to make his memories of Mamiya last forever. (It's not Nemuro Memorial Hall because Nemuro died there; it's called that because his memories are stored there.)
Either way, the result was a haunting. Anthy in the form of Mamiya stuck by Mikage (which is why she's been so tired--being two people at once must be exhausting), and the two preserved memories--ghosts, in other words--lingered on the campus, stuck in their pasts.
(I mistyped the preceding line as "stuck in their pasta." VERY different show, that would be.)
The question then becomes, what was the point of all this? What did Akio gain by manipulating Mikage into manipulating the students?
Well, it's hard to say what he gained, but something did change: time is now even more broken. Mikage never existed to begin with, and the memories of the Black Rose Saga are, for Utena, seemingly erased? Did the Duels happen without them ever figuring out who was behind them? Or did they all just get a couple months' break from dueling?
More importantly, Miki remembers that the building is called something Memorial Hall... But if it wasn't rebuilt after the fire, that means it was named that BEFORE the event that caused it to be renamed!
So now the question shifts: Who and what ARE Akio and Anthy? It's now clear that Anthy's insight and the strange events that happen around her aren't coincidental... She has power of some kind, and she's actively working with Akio. But to what end? How much is her involvement willing and how much is it coerced, given the abusive sexual relationship between them? (Her smile at the end of this episode suggests that she did derive some pleasure from manipulating Mikage.)
And what on Earth could their goal be, that breaking time is part of it? Are they after eternity, or something else?
I kind of perversely love this episode? I mean, objectively it's not very good, but the sheer audacity of doing a clip show made of clips from filler episodes fills me with glee. The only clip show I like better than this is the Greatest Clip Show of All Time, from Clerks the Animated Series. (It was the SECOND EPISODE. They only had one clip. They showed it about 20 times over the course of the standard-issue clip-show frame story.)
Anyway, this makes perfect sense. It's the end of the arc, so we need a clip show. But the conclusion of the Black Rose Saga retroactively deleted the entire plot, so what can we show clips of? Why, the not-plot, obviously!
There's also something a bit subtler going on, too--the last episode showed that Anthy has (currently vaguely defined and of unknown origin) Powers, that her manipulations and insights are NOT an accident but tied in directly to the weirdness of Ohtori Academy. This episode thus does to the Nanami Has Wacky Animal Adventures episodes what the previous clip show did to the Student Council arc, namely recontextualize it to show how it all tied together into an ongoing plot orchestrated by a hitherto unsuspected shadowy figure.
EVERYTHING bad that has happened to Nanami thus far is Anthy's doing. Remember the elephant she drew in the margins of her textbook during the study session with Nanami and Miki? And now we see that she fed her curry to the Barbershop Trio and elephants, creating elephants that wanted to pursue Nanami.
This is a silly, pointless filler episode--TVTropes calls it the only entirely dispensable episode of the series. Yet it's also the episode that demonstrates PRECISELY how powerful, dangerous, and frankly sadistic Anthy can be when provoked. She is not the innocent princess--but that does not necessarily mean that she is pure evil either, of course. Thus far there have not been any purely good or purely evil characters in this show--even Mikage was more misguided than malicious in the end, and Akio, for all that he is a sexual abuser and Mikage's puppet-master, has also been giving Utena actually pretty good advice all arc.
(Also, surprise return of the monkey-catching robot, who carts C-ko off into space in a ship that looks suspiciously similar to the one A-ko and B-ko left in at the end of the last arc. Does that mean we're going to get a D-ko taking over Shadow Play duties? Or Shadow Play Girls In Space? Only time will tell...)
Oh man. So much momentous stuff happens in this episode. The new arc really kicks off with a bang. Too bad it then immediately loses all momentum while it spends the next six or seven episodes cycling through the contractually obligatory duels with all the student council members. Have I mentioned that I really dislike the Car Saga enough times yet?
So, big revelation number one: Akio is named after the Japanese name for the Morning Star, and I'm just going to quote (warning: the text I quote in the next few paragraphs is safe, but the rest of the article contains extensive spoilers for the Madoka Magica movie, Rebellion) myself on this:
There is a recurring myth in the ancient Mediterranean. In it, the Shining One (Hebrew: Helel, Greek: Phaethon) tries to usurp the Sun or the supreme deity, and is cast down or punished for his presumption. This is a familiar myth in our culture, due mostly to the Greek version. The Semitic version is less well known, in large part because one of the few written references we have to it has been lost in translation, Isaiah 14:12-15 (NIV version):So that's the first big revelation: Akio's relationship to Dios, whose name comes from the Latin for God. Akio is casting himself here as the noble Satan from the common misinterpretation of Paradise Lost, who deems it better to "rule in hell than serve in heaven." Of course, in the actual epic it's blatantly obvious that Satan is expressing sour grapes and trying to look good in front of his followers when he says that--it's still open whether Akio is the same.
"How you have fallen from heaven, morning star, son of the dawn! You have been cast down to the earth, you who once laid low the nations! You said in your heart, “I will ascend to the heavens; I will raise my throne above the stars of God; I will sit enthroned on the mount of assembly, on the utmost heights of Mount Zaphon. I will ascend above the tops of the clouds; I will make myself like the Most High.” But you are brought down to the realm of the dead, to the depths of the pit."
The English term "morning star" is being used to translate the Hebrew Helel. We can imagine the mythology here fairly easily--the brightest star in the sky, refusing to share its place with the other stars, and instead jumping up into the sky at dawn, ahead of the sun. Then at sunrise it is wiped away, only for the story to repeat the next day, an endless cycle of celestial hubris.
Of course, most of us are more familiar with another translation, the King James, and another variant of the myth, which uses the Latin name for the morning star: Lucifer.
His role as a Satan-analogue is even clearer in the car scene, where he tempts Saionji by showing him the world. It's a pretty blatant reference to the story of Satan doing the same to Jesus, only with Saionji it, y'know, works.
Of course, he and Dios are also the same. The last two lines of the egg speech from Demian, which the student council always leaves out, are "The bird flies to God. That God is Abraxas." Abraxas is the two-faced god who created both good and evil.
Second big revelation is that apparently the Black Rose Saga DID happen in some sense, even if no one except Anthy and Akio remembers it: First and most obviously, the gondola appears. It appears that, just as Mikage was used to create the path to the dueling arena in the first place, he was used again to create this new path, which apparently leads to a higher order of duels.
More subtly, Anthy and Utena are now close enough for Anthy to draw Utena's soul sword the way the Black Rose duelists drew the student council's. Notably, however, it is Utena who wields the sword; Mikage mentioned that most people aren't strong enough to wield their own swords, but Utena apparently is.
Trigger warning: discussion of rape in the next two paragraphs
Third revelation is that Anthy definitely does have a will of her own, confirmed by the fact that Saionji says she doesn't. Er, I mean, confirmed by the fact that she initially resists Akio at the end of the episode. So he rapes her. (There are fan theories that Akio is LITERALLY the Devil, but I think that cheapens his horrifying actions. He is a man, who chooses to do incredibly evil things to children. Pretending he's some kind of supernatural, cosmic force is too easy, it lets us pretend that evil is somewhere Out There instead of right in here.)
(I am honestly not sure whether to call their previous sex scenes rape. The relationship is clearly abusive as fuck, but that doesn't necessarily make the sex nonconsensual, and I'm not sure how age of consent applies to someone who may or may not have been 14 for the past several centuries or longer.)
Trigger warning over
Going back to the car, it's common in the fandom to view it as a metaphor for sex. I think that's true but incomplete. No one in Ohtori is allowed to grow up (which is one of the most horrifying things I can imagine). Akio is showing people trapped in a perpetual adolescence a glimpse of the adult world. Sex is definitely a part of that, but so are power, freedom, and sophistication. Notably, Nanami emphatically rejects the sex but accepts the temptation, so it must be more than just sex.
So, my interpretation is that Akio expected the Sword of Dios to vanish, but that Anthy helped Utena more than she was supposed to. I think this was a test of whether Utena has become strong enough to wield her own soul sword; the goal of the next series of duels is to refine that sword to the point that Akio can use it to open the Rose Gate after all. But then why is he upset by the end of this duel?
The only explanation I can see is that Utena was supposed to use her soul sword, but Anthy wasn't supposed to help. The fact that she does so not only means she choosing to help Utena of her own accord, beyond her role as the Rose Bride; it also means that she feels a bond to Utena as close as the Black Rose duelists to the people they pulled swords from--siblings, close friends, years-long crushes. Abusers depend on isolating and controlling their victims, so Anthy developing that kind of bond is incredibly frightening to Akio.