What's Wrong With the Prisoner of Azkaban Movie?

I love the Harry Potter films.  They'll never be the books, but as far as movies go, I really enjoy them.  However, there will always be a few things in each film that annoy me a bit everytime I rewatch the movie.  The end of Prisoner of Azkaban (PoA) is full of those things.

I have a love-hate relationship with PoA.  On one hand, it's been one of my favorite Harry Potter movies since it was released.  (Recently, it's been put into third place by Half Blood Prince and Deathly Hallows Part 1, and then there's the fact that Sorcerer's Stone will always be special because it's what made me a fan.)  However, I also have a lot of problems with it.  While I feel it's a good movie, they don't explain quite a few things that are important to the story.  So many people I know only watch the movies, and they're left extremely confused at the end of PoA.

I don't think the word marauders is mentioned once except in reference to the map.  That's a crucial bit of backstory that they never even address.  At the end of the movie I believe it's Remus who says something along the lines of, "The map never lies."  However, it's never explained how he knows this.  Furthermore, Harry, Ron, and Hermione never seem to wonder or question how he knows this, which doesn't make sense to me.

It's also never explained why Sirius and Wormtail are animagi.  Now, since Harry doesn't know about the Marauders, I can see him not really wondering that.  Even so, the Marauder's should have been explained, and the animagi thing should have come up.  That was a great bit of backstory.  One of my favorite bits of the PoA book.  I love learning about the Marauders.  Then there's the fact that, because the animagi thing is never explained, you never learn why Harry's patronus is a stag.  Again, I can understand why this wouldn't be of crucial importance, but I feel like it should have been included.

Including all of that backstory could have slowed the movie down, and that may be why the filmmakers chose not to include it.  However, I think they're creative enough that they could have pulled it off if they'd tried.  Maybe instead of just Sirius and Remus standing there talking, they could have done a flashback or something.  It wouldn't have mattered to me.  I just wanted it in the movie in some shape or form.  I think not including it was a really bad decision.

What's something that happened in the Harry Potter books that you wish had been included in the movie?