The Breakfast Club/WMG

Brian wanted to get stuck writing the letter.
When Vernon came down on them for skipping the assignment, Brian would get off scot-free. If Vernon tried to get him into trouble again, the report in his handwriting would clear him and probably put some suspicion on Vernon of his corruption; the other teachers would start watching Vernon a lot more closely. Meanwhile, the other four would think that he had been "sticking it to the man" along with them instead of doing the assignment like the sycophant they thought he was.
 * Early on in the film, he's the only one seen to be taking the assignment at all seriously. Considering that he's the Brain, it's possible he was simply interested in the question on its own merits.

There were only four students; Bender was the "unrestrained" persona of Brian.
The students didn't call him on his differing stories because of the things "Bender" had already made up. Two clashing stories don't seem like much when there are three other stories he insists are true.

The charge wasn't just a flare gun in his locker, but a flare gun set up to blow up in front of anyone who tried to get into his locker without disarmng it, which happened when a teacher noticed that his elephant lamp looked suspiciously like a water hookah when the lamp mechanism was taken out. Bender's locker was an empty pair of lockers on the other side of the school that he set up to avoid 1) being caught with a bag of weed in his locker, and 2) burning it all up when the trap was triggered.

Which and how much of their backstories were true is unknown. Odds are, he ran away a few months or couple of years ago and has lived in an abandoned house ever since. Any scenes where Bender insults Brian, such as the lunchroom scene, are just him mumbling and being surly and (to anyone listening) mocking the reaction of someone who might object to his insults. At the end of the film, Claire falls for Bender and Brian, since they're the same bad boy to her. The Brian persona writes his idea of a subversive note in which the "extra" character seemed like something he threw in for contrast against the popular athlete and "cool" criminal (like how the basket case contrasted against the princess).

They all killed themselves. Well, not Claire...
Detention is purgatory, place where the kids repent for their sins. The nerdy kid DID top himself, as did the Jock because he felt so ashamed for what he'd done. Claire went to the mall with her friends, the car crashed and she died. Allison had nothing better to do bt kill herself and Judd Nelson is Judd Nelson, so he killed himself too.
 * Carl could be Jesus. He guides the kids (and Judd) through detention, and does help them improve themselves, though mostly leaves it to them.

Anything from the pot smoking on was a hallucination
It was REALLY good pot. Explains the lack of logic in the last five minutes.
 * Alternatively, the narrator was unreliable. We get the film from the point of view of the characters, and the reason things don't make as much sense in the end is because they're still really, really high.

Bender was a cartoon character.
As Judge Doom said, "No toon, can resist the old Shave-and-a-hair-cut!" When Bender is hiding under her table, Claire hits the first five notes on the desktop, to which Bender replies with the two-bits! follow up hits.
 * Kiss my shiny metal ass!

They're all dead.
The characters exist in the DC Comics universe. They have died, and the entire movie is them gradually passing over and coming to terms with their own deaths. Alternatively, they were all alive and actually in detention, up until the janitor arrived, went nuts and killed the kids (he obviously hates them). Allison is in fact Death of the Endless, acting in her role as a psychopomp.

They're all dead and being judged by the statue.
It's watching over them, deciding... deciding....

Breeding pairs?
The kids and the few adults seen are the last few humans left. This detention scenario is brainwashed into them by caring aliens so they will breed.
 * Three guys and only two girls? Count me out of this re-population program.

The kids don't socialize with each other on Monday...
...at least not in school. They know that their respective cliques would tear them apart, so they pretend everything's the same to avoid conflict. But after school every day, they hang out with each other and away from their other friends.

Rather than becoming a bum, John Bender....
.... eventually writes a successful screenplay based on the events of the Saturday, in which his own counterpart is named "John Hughes"!

Bender did punch Vernon
The second half of the film was his hallucination to cope with going to prison after punching out Vernon.

Claire slept with all the men in the group.
It is heavily implied during the scene where Bender rips up the books, that Claire may have slept with Andrew at one point. It was also heavily implied by Bender (whom also guessed correctly that Andrew hated his parents.) that he slipped her the "Hot beef injection." She ended up with Bender in the end. Plus she did convince Brian to write the essay for them all, so he must have had something out of it.

Allison slept with Brian and Bender.
Bender claims to have seen her before. How else would she get close to Brian and steal his wallet.

Allison killed her parents.
Makes sense, she stole Benders knife and never gave it back, unlike Brian's wallet. Her parents ignore her so they wouldn't see it coming.

Brian's parents have connections with the faculty.
How else would he get Saturday detention for bringing a flare gun to school?

Brian's parents are pushing him to be perfect for selfish purposes.
It's appropriately cynical, and fits in with his mother's overall sleazy mien. Brian's mother and father don't see him as a human being, but as a means of earning prestige in Shermer. They grossly insert themselves into his academic process, and they surely take the credit for his successes. Furthermore, the higher the GPA, the more money you make. Think about that for a second.

Vernon goes to jail.
Brian secretly placed recording devices into the library and storage closet. Vernon's threat to Bender has been recorded. Why else would John smirk at Bender when he asked if he was threatening him. He knew about the devices and was just confirming it. The threat is placed all over the announcements on Monday. Vernon gets fired and arrested.
 * And then Ed Rooney gets his job.

Allison does end up running away.
She goes to New York, where she eventually changes her name to Marla Singer.

The movie is set in the same universe as Squee and Johnny the Homicidal Maniac.
Allison is in the same boat as Squee, in that her parents don't care about her and she clearly has a number of issues. She's also artistic, a skill demonstrated early on in the movie.