1) Isn't it a tiny bit early for Lupin to embrace Sirius as if they were brothers? Okay, Lupin does ask first whether Sirius "switched" (the secret-keeper deal), and he did see Pettigrew seemingly alive and well on the Marauder's Map. But up till that moment, he supposedly believed Sirius guilty just like everyone else did, and he hasn't actually seen Pettigrew transform back into himself yet. So wouldn't he suspect that Sirius and Pettigrew were still tricking him somehow--or both on the Dark Side, but feuding with each other--and demand a rather more in-depth explanation before hugging him? Still, the hug is such a great surprise moment, I hate to deprive them of it.
2) For that matter, why doesn't Sirius go to Lupin earlier on and tell him the truth? Or at least leave him a note advising him to take a good look at Ron's rat? If Sirius is sneaking in and out of Hogwarts, he could manage it (or have Crookshanks deliver the note).
3) If Harry sees his super-awesome scene-saving Patronus by the lake the first time around, then why don't the other changes he and Hermione bring about with the time-turner also happen the first time around? Why doesn't Buckbeak get saved? (Or do we know for sure he is actually executed the first time? Hmm.) Etc. Time travel never makes sense, and drives me crazy, which is why I don't write it, though it is fun to read or watch.
4) Anything you think I should mention in the condensed parody version? Now's your time to be fun and silly and potentially get your name in the credits. Meanwhile, Happy Halloween!