
Revealing mistake: After being dropped by the troll in the girls' lavatory, Harry then scoots backwards on his backside and it is apparent that he is wearing knee pads under his pants. (01:11:40)

Revealing mistake: During the Quidditch game, none of the players have shadows on the ground. (01:16:20)
Revealing mistake: Just after Harry gets back on his broom, the Slytherine seeker chases the snitch and he passes towers of (in order) Gryffindor, Hufflepuff, Ravenclaw, Slytherine, Gryffindor and Hufflepuff, on his left (this means Hogwarts is also to his left), when Harry flies up beside him. However, next shot as Harry slams into him, they still fly in the same direction, and the school is now on their right. Mistake with the background plate. (01:22:00)
Revealing mistake: When Harry is walking in the library's restricted section, you see the shadow of the library pillars on the bookshelf. If the light was coming from his lantern, there would be no shadow - the light is obviously from a spotlight elsewhere. (01:25:20)

Revealing mistake: When Harry brings Ron to see the mirror of Erised, the green side of the invisibility cloak is seen when they are running to the mirror, near the door they entered from. (01:33:55)
Revealing mistake: Harry, Ron and Hermione are at Hagrid's hut asking him about the hooded man and the dragon egg. The background behind Hagrid, which is the hut, is really behind him, but when it cuts to Harry, Ron and Hermione it is very apparent that the kids were edited in with their background, which is the school. (01:50:45)

Revealing mistake: When Ron is hit by the Queen during the chess game, the stunt double is visible on the horse just a few moments before he falls. (01:59:00)
Revealing mistake: During the chess game the Queen attacks the Knight's horse that Ron sits upon. In this close-up just before the spear actually hits the side of the horse, the large hole, used to aid the stunt, is visible in the belly of the horse between the stirrups towards the hind legs. This hole is not in previous shots. (Visible in fullscreen DVD.) (02:05:10)

Revealing mistake: At the end of the film, when Harry is leaving on the Hogwarts Express, and the overhead shot shows the train pulling away from the station you can clearly see that Hagrid is of normal height, as the train roof is much taller than he is. (02:23:40)
Chosen answer: There are several reasons. First, the position is cursed, so there is little reason to give Snape the job when he will not last any longer than all the previous instructors. If Snape did become the DADA instructor, something could happen to him that could result in his being harmed, having to leave Hogwarts, or be otherwise incapacitated in some way; that would render him useless to Dumbledore as a double agent. Also, Dumbledore trusts Snape, but putting him in an environment where he is teaching about dark magic on a daily basis would be too tempting and emotionally compromising to someone who had been so easily seduced by the dark side. He could possibly relapse. It would be like having a recovering alcoholic work as a bartender. Of course, he does eventually become the DADA instructor, and lasted no longer than his predecessors.
raywest ★
In the movies it is never mentioned that DADA role was cursed by Voldemort.
This is true; though it doesn't say it's not either. With trying to fit 7 long books and years worth of pages of HP information in 2 and a half hours; as long as the movie doesn't say it's not cursed, with our knowledge, there is no problem with reporting that it is. Even directors of non-book movies do this all the time; leave background information out that helps explain things they just didn't have time so they explained it behind the scenes.