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.
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?