Best Adapted Screenplay
I find it remarkable that this movie won an Oscar for best adapted screenplay. Adapting the story to a Boston setting? Fine, that was done reasonably well. But the actual plot? One of the major changes was merging two of the only female characters from the original movie into a single contradictory mess - one who has spawned a number of threads here from people who likely haven't seen Infernal Affairs and yet can still see that there's something off about her.
The biggest change is the ending. Infernal Affairs had a poignant and thoughtful ending. The Departed's ending is cheap, juvenile, nihilistic garbage.
Beyond that, there are plenty of more minor changes outlined in some of the top reviews here that make the main characters in the Departed one-dimensional and the plot entirely lacking in nuance. In fact, I can't think of a single change that actually improved the screenplay from Infernal Affairs, which was very good but not flawless. So if this was the best adapted screenplay of that year...