As usual, Draco spends most of Harry Potter and the Prisoner of Azkaban being an insufferable bully, with a focus this year on being needlessly cruel to Harry about his reaction to the Dementors. It's clear that time is not mellowing Draco (yet), and that he still has it in for Harry and his friends.
Draco isn't a particularly big part of this book or film, either - while he does pop up from time to time to be mean to people, he doesn't actually have a huge impact on Harry and his friends - and when they do interact, much of the time Draco actually ends up helping the Golden Trio, even if this isn't the intention! Overall, his decisions end up being good ones, even when they come from a less-than-wonderful impulse.
Taunting Harry Over The Dementors
Draco's main purpose in this installment of the Harry Potter franchise is to continually taunt Harry over his reaction to the Dementors. It's a particularly cruel thing to do, especially considering that Harry's reaction is so strong because of the tragedy that he has experienced in his young life! It may seem that this action has no positive effect, and is just another example of Draco being a bully, but that wouldn't be quite accurate.
In fact, Draco's taunting may actually be what spurred Harry to go to Lupin about the Dementors - and it is this that not only teaches him what he needs to know about the Azkaban guards, but that also allows him to save his own life (and Sirius', too). It's possible that had Draco said nothing to Harry, he would have still be affected enough to learn how to deal with the situation, but Draco may have unintentionally led Harry to a life-saving spell.
Accusing Hagrid Of Being Dangerous
Most fans would see Draco's treatment of Hagrid as absolutely abhorrent - he intentionally goes against his professor's instructions with a dangerous magical creature, and then accuses him of negligence when he is injured. Draco is seen to be completely overplaying the injury, too, pretending it is far worse than it is, in an attempt to get Hagrid fired - which seems, overall, to be a series of terrible decisions.
However, Draco's bad intentions backfire, and this decision actually ends up helping the Golden Trio hugely in the end. Had Draco not been such a bully about Buckbeak attacking him, Buckbeak would definitely not have been tied up in Hagrid's garden, conveniently available for Sirius to escape on. In fact, without Buckbeak there, it's unlikely that the Trio would have been able to let Sirius escape at all!
Telling Snape That Harry Was In Hogsmeade
After Draco realizes that Harry is in Hogsmeade without permission, he runs to Snape with the intention of making Harry's life more difficult. What he doesn't realize is that tattling on Harry will set in motion some extremely important events!
Because Snape goes looking for Harry and tells him to turn out his pockets, Lupin ends up confiscating the Marauder's Map - and if he hadn't, he would never have known that Peter Pettigrew was back, or figured out that Sirius had been set up. Without this, Sirius' story would have turned out very differently - and likely, not quite so well.
Dressing Up As A Dementor
Draco and his friends' decision to try and dress up as Dementors to scare Harry was a ridiculously childish and cruel one - but yet again, Draco's mean decision ends up helping Harry in the end! Because Harry had been prepping with Lupin, he was able to cast a strong Patronus over the Slytherins, gaining him extra confidence, not stopping him from winning the game, and because Draco was caught, Slytherin House lost so many points that they couldn't possibly win the House Cup.
This was a terrible decision as a Slytherin, then, but for the Gryffindors and Harry, this was a great choice - and one that let them win at the end of the year!
Mocking Hagrid
Admittedly, of all Draco's choices, this was one that definitely turned out the worst for him - but made for one of the most satisfying scenes in the franchise... as his insults to Hagrid led to Hermione punching him in the face! Draco is clearly just continuing with his usual bullying meanness when he starts making fun of how upset Hagrid is over Buckbeak's situation - and Hermione absolutely cannot stand to see it.
Watching her punch Draco in the face is immensely satisfying, but she would never have done it had he not pushed her in this way. More than simply a satisfying scene, though, this shows a side of Hermione that is important, and that isn't previously brought to light. Her strength isn't just in her books, and she shows here that she truly is a Gryffindor - rash, strong, and willing to throw down when someone deserves it!