Other mistake: When Jack Nicholson is talking to the manager of the Overlook Hotel, the manager mentions the death of two girls aged 8 and 10. When Danny sees visions of the two girls they are unmistakably twins, not different ages. A quick look at the IMDb (http://uk.imdb.com/title/tt0081505/fullcredits) proves they are - Lisa and Louise Burns, both born in 1968.
Continuity mistake: If you compare the map of the maze posted outside on the actual maze (visible when Wendy and Danny first run inside it), to the model of the maze Jack looks at in the hotel which pans down to Wendy and Danny walking through it, the two maps look nothing alike.
Continuity mistake: When Jack is chopping at the bathroom door with the axe, he completely breaks through the right side panel. After the shot of Halloran arriving in the snow cat, we see Jack at the door again and there are a couple of large wood slivers lodged in the right panel.
Continuity mistake: In the scene where Hallorann is talking to Danny over ice cream, when the shot pan to Danny, the amount of ice cream stains he has on the side of his mouth changes.
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.
Continuity mistake: After Jack kills Halloran, there is blood on the blade of the axe, including the next couple of scenes chasing after Danny. However, when they get into the maze, the axe blade is bright and shiny with no traces of blood.
Continuity mistake: When Wendy is trying to escape through the small window, she leaves the room with the lights on, but in a view from outside the lights are off, then Jack passes by and the lights are on back again.
Continuity mistake: When the Danny is meeting with the chef in the kitchen, and Danny is eating ice cream. The amount of ice cream in the bowl changes from a little to a lot.
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: When Shelly Duvall is crying, backing up the stairs and swinging a bat at Jack Nicholson, the positions of both of their arms and the bat change dramatically as the camera shots switch back and forth between them.
Continuity mistake: As Jack talks and yells to Wendy at the writing spot, a chair appears behind him between shots.
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.
Revealing mistake: In the shot just before when Jack finishes axing the bathroom door, one of the broken pieces of wood is resting against the camera.
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.
Answer: Effectively, Danny's shining is what brings the hotel to life. Because he has such an incredibly powerful shine about him, all these weird ghost things in the hotel are able to materialize and reveal themselves. These weird ghost things are always present to some degree, and those people with a small degree of shine get glimpses of them - like Dick Hallorann. (It's not quite made clear in the movie, but Dick saw the woman in room 237 in the book). However, Danny's shine is so great that he gives these forces enough life to appear to those without any shine, people like his father and mother. As it's the hotel that's slowly driving Jack crazy, and the hotel gets its power from Danny's shining, then I'd say there's definitely a connection between Jack's insanity and Danny's abilities. In the movie, it's not as clear as it is in the book, but Jack is effectively possessed by the hotel. He's not a flawed drunk with an anger problem who loses his mind because of isolation. He's a flawed drunk with an anger problem who's doing the best he can, until the forces of the hotel get inside his head and make him lose it.
If Danny's shining is what brings the hotel back to life, does this mean that all the previous "Jacks" had a son or daughter with the shining too?