Mai-HiME/WMG

Mai accepted the Obsidian Lord's proposal.
This technically doesn't contradict anything: she received the power to rebuild the world as she wanted it, with all her friends alive and happy. As an added bonus, her acceptance of the Obsidian Lord is now a Ret-Gone event, leaving her free to do whatever with her love life.

The whole final episode is Mai's delusion, similar to the one she was experiencing under Yukariko's influence: an effort to imagine a "better" world where she's not a HiME.
If you want a Downer Ending, this option is for you.

The whole series after episode 8 is Akane's delusion.
Read this.

Episode 15 wasn't The Worf Barrage for Kagutsuchi; both it and Mai did indeed die, but they were resurrected by Mashiro.
Note how, after Artemis fires at Kagutsuchi, it is engulfed in a fireball and drops from the sky... until Mashiro, having recovered from her shock, whispers "Mai-san", after which the fireball stops falling, Kagutsuchi emerges and regenerates, and a stream of fire detaches from the fireball and transforms into Mai. Presumably, both Mashiro and the Obsidian Lord were stacking the deck in Mai's favor for the There Can Be Only One Festival; she was one of the primary chess pieces of their dueling Xanatos Roulette. This is also why she's allowed to change her Most Important Person.
 * Another MIP was chosen for her after Takumi's death because he was slain after Akira was defeated, and he shared life force with both of them. A situation like that repeated itself immediately afterward, with as her chosen; but he's also bound to . So, yeah...the Gods liked messing with Mai's head and heart.
 * It's implied that Takumi's desire for independence was starting to form a rift between him and Mai, which, combined with Mai gettinh closer to, caused her to switch Most Important People before . This doesn't necessarily rule out her MIP switching to someone else after her previous one's death, but it's less likely that happened when.
 * Interestingly enough, in the manga, gets another Key after her first one dies, but in this case, she barely cared for her first Key at all, and the rules may be somewhat different (Yuuichi becomes Natsuki and Mai's Key after they first meet).

As above, but Kagutsuchi resurrected itself.
This would explain why it's implied in episode 25 that Kagustuchi's user has won every previous Festival. How can you finish off something that just comes back upgraded when you kill it?
 * It was only implied that Mashiro used Kagutsuchi in the previous Carnival. Nothing is known about older ones. But yes, that is one insanely powerful beast.
 * After revealing Mashiro won the previous Festival, Reito offers Mai the world in exchange for her hand in marriage. Mai refuses, citing what a cruel bastard he is. Mai (who is being seen from Reito's point of view, mind you) immediately fades into a flashback of Mashiro in battle-torn shrine maiden robes standing in the exact same place as Mai giving the viewer exact same cold stare as Mai. After the flashback ends, Reito mumbles something to the extent of "Kagutsuchi users are always stubborn." That's not simply an implication.
 * It does have a blatantly obvious phoenix theme going in that scene.

Nagi is a representative from Earth's local Hell who brought Mashiro with him.
The Obsidian Lord is some kind of Space Demon Overlord who summoned Mashiro from Hell for the "flavour" of the last Festival. Nagi came along to help organize the deal; while the death and destruction is amusing, it's not his job. Thus, when the Obsidian Lord's defeat concludes the deal, Nagi escorts Mashiro back to Hell.

Natsuki's original "Most Important Person" was her mother.
However, with her dead long before the Festival began, Natsuki kept insisting that she had nothing to fight for, since, like Mai, she was trying to avoid getting romantically involved with anyone. Therefore, another one was chosen for her in.
 * This isn't so much a WMG. She pretty much realizes this before/during her final battle with  and accepts what's going to happen.

Shizuru was Brainwashed the whole time she went crazy.
She (briefly) gets what look like Mind Control Eyes after attacking Haruka and Yukino, and then walks away from the scene speaking in a dull, flat tone, expressing the desire to take out anyone that gets in Natsuki's way. Later, Nagi and the Obsidian Lord are seen reveling in the destruction that she's causing. Since the Obsidian Lord is, he probably had the perfect chance to administer his "treatment" offscreen, the same way he did with Mikoto.
 * Furthermore,.
 * Shiho
 * If Shizuru were brainwashed, why would the series

Could it be an AU of Metal Gear Solid?
You have an Ancient Conspiracy explicitly said to be able to control the US Presidency, with one of the key characters involved in it being called Searrs. Now you have the Patriots, who have also been said to control the US Presidency; and the President is called  George Sears... So there is an "r" off, yeah; maybe Sunrise wanted to dodge the lawyers from Sears & Roebuck. All those HiME powers are Nanomachines - hey, it worked for MGS, and the similar WMG for Code Geass was also rather far out.
 * The Elseworld sequel, Mai-Otome, explicitly uses nanomachines summon their powers. Coincidence, or teasing of Konami's lawyers?

It was all Kiyohime's fault that Shizuru went Psycho Lesbian.
We know that it's possible for a CHILD to carry across Festivals, passing from one HiME to another, since Kagutsuchi was Mashiro's CHILD in the previous festival. Shizuru also got one like that, the one who in some previous festival had formed the basis for the Kiyohime legend. Tied to a Child with that much history regarding scorned women, she naturally went nuts at the faintest hint of rejection.
 * It's specifically stated that the Hi ME's emotional state and the form of love they hold toward their most important person determines their Child's shape, not the other way around. Granted, though, even that guideline wasn't all that consistent in application.

The Obsidian Lord is Akio
After, Akio started the HiME Festival (which is essentially a duelling tournament) as a method of creating a new Rose Bride, using the same method of tempting the winner with whatever they desire in return for their servitude.
 * Following on from this, Tate and Shiho are reincarnations of Touga and Nanami.

Normal!Shizuru and Psycho Lesbian!Shizuru were originally two separate characters
Given Psycho Lesbian!Shizuru's radical change in characterization from what she did previously, it's entirely possible that they were meant to be different individuals, but the writers didn't want to have to introduce a new character so late in the story and merged the roles. That character would most likely have been similar to (if not a counterpart of) Tomoe from Mai-Otome, and the producers may have created her to serve as the obsessive Psycho Lesbian without necessarily offending Shizuru's fans.

Mikoto was always Mai's "most important person".
Despite what she said, the fact that she could still summon her child after Yuuichi's death proves that the person she cared most about was still alive. Mikoto is the only real candidate. Note also how happy she is when she discovers that Mikoto is still alive in Episode 23, just a day or so after Mai tried to kill her and after Mikoto was responsible for Takumi's death.
 * As a possible explanation of this, it may be that a HiME's powers rely not the person for whom they care about the most, but the person about whom they cared the most when they released their powers for the first time. And Mai used her powers for the first time to save Mikoto's life, as well as her own.
 * When Yukariko first manifests her Hime powers, she's defending Aoi from the vampire Orphan, yet Ishigami becomes her MIP. Similarly, while Natsuki was already friends with Shizuru when she got her powers in "Natsuki no Prelude," Shizuru wasn't anywhere nearby when she first accepted Duran; Natsuki ran into Akane on the way there, but otherwise, no one except Natsuki and Nagi were present. Nao and Midori's most important people were unlikely to have been anywhere near where they were fighting Orphans during the time in which the show took place. This theory is thus unlikely.

The person Nao wanted revenge on in the Blu-Ray special was Yukariko and/or Ishigami, not Shizuru

 * While the girls are force-feeding Reito spicy food in revenge for what the Obsidian Lord did, Natsuki sees Nao and Yukino sitting it out, and Nao points out that she has someone else to seek revenge on. Natsuki assumes that this is Shizuru, but given that Yukino (who also lost her Child and most important person to Shizuru) apparently disagreed with Nao before going off to give Reito a spicy hot dog, it's possible that Nao had someone else in mind. Since Nao knows why the Hime attacked her in the battle in which she lost her eye, she might have wanted to go after Yukariko (for faking her injury) or Ishigami (for making her do it).