Across the Universe (novel)/WMG

Max and The Joker are somehow related.
The self destructive habits, the weirdly nasal voices... and the hair. Cryogenics may be involved. Perhaps why the Carrigans seem so irresistibly called to Gotham New York City... This may also explain where on God's green earth Puddin' stole his fashion sense from -- Sadie, of course.
 * Maybe the Joker is Max.

Max becomes a psychopath during the war
What Max is majoring in at Princeton is never stated in the movie. There is a medical school at Princeton. Jude, Lucy, and Prudence all share names with people in Beatles songs. The Beatles songs are in the movie. There is a Beatles song about a person named Max. This song is not in the movie.
 * But he's a Carrigan, not an Edison... or is he? Unless he has an Embarrassing Middle Name.
 * They did squeeze in a reference. When Max and Jude are looking at the apartment, Sadie jokes that they may have killed their grandma with a hammer, and then goes on to ask them if they did.
 * He also mends a fan with a silver hammer.

Max was a psychopath BEFORE the war.
The film is how Lucy would like to pretend it happened. Remember, they look like clean cut boys, but he could have murdered his granny with a hammer...

Prudence has been cursed to always be at the wrong side of a Love Triangle because she is only attracted to people who are unavailable.
Every character that she showed even a remote longing for was involved in a relationship with another person (the cheerleader, Sadie, and possibly Jude or Lucy depending on the interpretation of two scenes, one deleted). There was likely some emotional unavailability or another, similar distancing for the girl she met in the circus, since we see literally nothing of her personality despite Prudence's return and introduction of her (which may have propelled a "running away to join the circus" backstory).
 * Well, she does hook up with the redheaded contortionist, which sure as hell sounds like she got her happy ending.
 * As well as her "happy ending".

Everything after the protesters set off the bomb at the rally is a figment of Jude's imagination.
Think about it. The newspaper explodes, and he's on the same beach as he was in the beginning, where he was telling "his story." The story's over. Then he imagines Max singing to him, has absolutely no trouble getting a visa to enter America despite having been deported just months before, and then the radio talks to him! He asks, "Is that Sadie?" And the Radio Man says "You got that right." He's imagining the whole thing. He's still in England, sitting on the beach.

Max was in the US Army's Surrealism Battalion
The scenes of Max in Vietnam aren't an artistic representation of the horrors of war. Max was inducted into a special unit of the Army tasked with battling strange nightmarish things beyond our puny human mind's comprehension.

All six of them are dead by the end.
Sadie and Jojo just followed their natural Joplin/Hendrix paths, Max expired in the army hospital, Lucy was still in the building when in blew up, Prudence was depressed and lonely enough to off herself, and Jude decided to follow suit after getting the news about Lucy and Max. Everything from Jude's legal passage to the rooftop concert sequence is their reuniting in the afterlife.
 * That is both really depressing, and really beautiful.
 * It would certainly explain why the microphones in the rooftop concert scene are modern mics--the afterlife is outside of time, thus anything from anytime can exist within it.
 * So why didn't Sadie and Prudence get year 2022 Luxospeak 7s (widely considered to be the best affordable microphones before the second world currency changeover in 2341), and Jude have Paul Mcartney's microphone?

Max was part of a unit that our own military bombed with experimental hallucinogenic gas.
However, since most of his squadron survived their suicidal battering-ram run into Charlie's camp but were completely uncontrolled, it was decided to be ineffective both for weaponization and Status Buffs. The heroin that the Selma Hayek nurses gave them was meant to help the withdrawal, and since the whole team had been disqualified from further service as a result of the experiment (or were 4-F'd recruits for any reason but flat feet) they were also treated by a crazy-dancing witch doctor (the military couldn't very well use active troops to test for the effects of mysticism on curing neurochemical and emotional trauma).

Max was hot for Jude.
Evidence For: He asked if Jude believed in love at first sight the night they met and treated him just as closely as his fratmates, it was not confirmed onscreen that he either went steady or slept around with any females (commenting on Sadie's sexiness proves nothing), he gave homosexuality as one of the Long List of reasons that he was prepared to back up for not being allowed in the army, and he was the only one waiting for Jude at the end when (of his friends) only Jojo, Sadie, and seemingly Prudence were required for the concert. Evidence Against: He gave homosexuality as one of the Long List of lies that he was prepared to back up for not being allowed in the army.
 * Prudence mentions to Max's sister in passing that she doesn't sleep with Max anymore, and Max later mentions that he thinks she's still hung up on him (everybody else rolls their eyes at him). So really, this one could go either way.
 * It's not explained very well in-movie, but the scene is actually more like this: Prudence tells Lucy that she's now living with Max and Jude, Lucy is unnerved by that (she's into Jude, but they're not together, so she's worried that Prudence got to him first), and Prudence, in an attempt to assuage Lucy's fears, says, "I don't sleep with them anymore", (as in, she no longer sleeps with men). Lucy, being rather naive, doesn't take it that way, thus later referring to Prudence as Jude's girlfriend. So, long story short, Prudence never actually slept with Max.
 * Jude does mention that he loves Max, but he could have meant it in more of a bromance kind of way.
 * The aformentioned "long list of lies" actually contained at least some truth, based on a 'blink and you'll miss it' scene earlier in the film - in the scene where Sadie's getting dressed and Max comments on it, Sadie tells him to put her shirt back when he's done, and he agrees to. So the whole 'cross-dressing' part wasn't completely false. Doesn't really prove much, but it kinda makes you wonder what else may have been true...
 * Which brings us to...

Max dies of lung cancer
If only they had actually done an x-ray, they would have found that spot on his lung...

Kurt Cobain's soul and being somehow transferred into Joe Anderson.
Just gotta say, they look really really alike. It's kind of scary.

Max killed civilians while he was in Vietnam.
During "Across The Universe/Revolution", we see him screaming while spraying gun fire off-screen. When he stops firing, he has a look of horror on his face. The next shot we get is the Mind Screw of the women dancing on the water before they all fall into it. The look on the last woman's face is... unsettling.

The movie takes place in a universe where The Beatles do not exist.
But most of the other things we know and love (such as strawberry fields) do, albeit modified by the lack of Beatles. Among other things, Julie Taymor directed a Jukebox Musical film featuring songs associated with Elvis Presley.