There are millions of mistakes in the First Book -
Continuity: When Harry goes to take his seat after being sorted, he sits opposite Hermione. In the next cut he is seated beside her.
Crew or equipment visible: The mechanism which makes the Quidditch box shake can be seen when the box falls over.
Incorrectly regarded as goofs: Platforms 9 and 10 at Kings Cross Station are not mainline platforms in the main part of the station, but are actually smaller, suburban platforms. This was an error made by author J K Rowling, though, who intended the Hogwarts train to leave from the main part of the station (she mixed up the geography of King's Cross with that of nearby Euston station) and so the film uses platforms 3 and 4 rather than the smaller platforms 9 and 10.
Miscellaneous: As the three children run across the field to Hagrid's hut, Harry says a few lines ending with "...why didn't I see it before?" Hermione is mouthing Harry's lines with him.
Factual errors: The snake that Harry talks to blinks. Snakes don't have eyelids, making it impossible for them to blink.
Factual errors: Each owl's wing beats can be heard. In fact, owls' wings make no sound.
Continuity: When Harry is taking notes in Snape's class his handwriting is small and neat. When seen from Snape's point of view it is large and sloppy.
Crew or equipment visible: When Harry, Ron, and Hermione are struggling in the Devil's Snare, a puppeteer can be seen on the left of the screen, working at least some of the masses of tendrils.
Continuity: During the train journey, Ron's hair is parted in several different places.
Crew or equipment visible: The shadows of a cameraman and a camera are visible on the wall in the Mirror of Erised scene. (This Could be Dumbledore)
Anachronisms: In the flashback to when Harry's parents were killed, young Harry is wearing a shirt with Blue from "Blue's Clues" (1996), a show which predates the scene by several years, on the sleeves.
Continuity: Harry's glasses sometimes have lenses, and sometimes don't, as do Dumbledore's.