All around the themes and ideas driving the characters are quite mature. I think it would allow them to be more uninhibited, and thus do more justice to the book when telling the story and showing certain things if they made it PG-13...but I don't think that will keep kids from watching it and people from talking about how it wasn't for kids.
Some things that could get a little well...
Spoiler:
*The snake coming out of Bagshot
*Pettigrew strangling himself
*Snape's Death
I wish they would make it R.. that way it could be more graphic and u could get a good feel for it.. but many fans are children so i doubt it will be R.. i hope it will be tho..