Continuity mistake: In Harry's first Quidditch match, Gryffindor scores the first goal, then we see the commentator announce the goal and change Gryffindor's score to ten - making a goal worth ten points. Soon after, Gryffindor score again. We then see Slytherin score a goal, then another. They then score a third goal, and the commentator changes the score to 20 all, but it should be 20/30.
Other mistake: Near the beginning, when the Dursleys' house begins shaking, none of the objects fall nor do the curtains shake.
Revealing mistake: When Harry, Ron and Hermione are making their way back to the Gryffindor common room, Ron says 'She knows more about you than you do', to which Harry replies 'Who doesn't?' The "solid brick" staircase moves so that they have no place to go but the third floor forbidden corridor. If you pay attention to the staircase it can be seen that there is a good gap between the staircase and the one it connects to when it moves and that when Harry, Ron and Hermione run off the staircase to the corridor the staircase made of "solid stone" does an awful lot of shaking.
Other mistake: Percy Weasley is obviously talking to the Gryffindor first years when they first enter the Gryffindor common room, but there are too many first years. There are 5 boys and 5 girls in each dormitory, so 10 first years in each house, but in the shot there are obviously almost 20 students there, not including Percy. (00:47:30)