That's not classified as a mistake because it's book to movie transition related. Sites only list film mistakes made in the making of the production, not the adaptation of it.

Like the Minister said, they don't arrest minors for blowing up people so they'd hardly arrest them for doing their homework!!! Even in the book, PoA, we learn Harry has homework to do, which he cant becuase his stuff is locked away, but surely magic homework involves the use of a wand?!

The law is in place for magic used in front of and in the prescence of MUGGLES. Otherwise, magic is permitted, perse, I'd imagine, for homework.