Continuity mistake: In the scene where Jack is telling Danny he would never hurt him or his mother, towards the end when the camera is facing Danny, you can't see Jack's right hand and can assume that he's leaning it on the bed; but when the camera moves back to Jack's face it is now around Danny's shoulder.
Other mistake: When Stuart Ullman is showing Jack and Wendy their quarters, there is a window on the wall to the right across from the bed. However later, when Jack tries to break into the bathroom with the axe and Wendy puts Danny through the window onto the hill of snow, their quarters is not on a corner of the hotel, which the aforementioned window would suggest. (00:22:45)
Deliberate mistake: Although Kubrick might've done this on purpose to show that the Overlook is unusual, as Jack is walking to the office to meet the manager, there is a left turn ahead, leaning to another hallway. When he goes into the manager's office, there's a window behind his desk that shows trees outside, but it shouldn't be there because that's where the hallway is.
Continuity mistake: Wendy is smoking a cigarette when Danny starts screaming, then she runs into the bedroom and opens the door, and doesn't have the cigarette.
Continuity mistake: In the scene at the beginning of the film, when Doc and Mr. Hallorann are eating ice cream, if you pay attention to Danny's hands, they move from folded in front of the ice cream bowl, to the back, and so on. They move about 5 times, each different.