Another example of redemption in Harry Potter and the Prisoner of Azkaban is Buckbeak the hippogriff. Buckbeak is really an elegant creature that requires certain rules be followed when approaching him. Malfoy does not believe Hagrid when warned to stay away from him so he runs up to Buckbeak and in turn gets thrown to the ground and is mildly injured. Of course Malfoy wants the creature destroyed so he complains to his father and Buckbeak is sentenced to death. Harry, Ron, Hermione, Hagrid and Dumbledore all know that Buckbeak is innocent and in the end free him and he carries Sirius off to freedom.

I guess I would pick Sirius Black and Remus Lupin as the examples of redemption in this book.

I think that you can argue that Lupin is redeemed to some extent in this book.  He has been shunned because he is a werewolf but Dumbledore brings him back to teach.  Of course, he loses his job at the end of the year, but in later books he'll be back and so he's clearly rejoining society to some degree.

More than that, we see the redemption of Sirius Black, at least in the eyes of Harry, Ron and Hermione.  Instead of being a hated and feared Deatheater, he is now Harry's beloved godfather.

I suppose you can say that Crookshanks is redeemed over the course of the book as well.  At first he seems like the real bad guy always trying to kill Scabbers.  But then at the end he is revealed as a hero of sorts because he realized what Scabbers really was.