Continuity mistake: When the reindeer gets into the house and runs around, it knocks over a TV set. All of the magazines that are on top of the set come crashing to the ground, including a TV Guide with "Get Ready For A Fabulous February" (or something like that) in big letters on the cover. Interesting since the movie is set around Christmas time.
Continuity mistake: When Jessica sits on Santa's lap in the department store, and asks for the real Santa's help to assist Prancer, she pulls down Santa's beard a bit. In one shot, the beard is definitely below his nose, after it is pulled. In another shot, the beard is right up under his nose. There are various shots where the beard is up one second and down the next.
Continuity mistake: When Jessica goes to the barn to investigate the banging, her hair is stringing in her face in one shot, and then in the next, it's brushed to both sides of her face.
Continuity mistake: Near the end, when Jessica and her father are taking Prancer to the mountain, within the three shots that it takes to show Prancer getting off the truck, walking around, and running away, he has his bells and bridle on, then off, then on again.
Continuity mistake: When Jessica comes out to their barn to investigate the noise, in one view, her hair is all brushed out of her face. Then the view changes, and her hair is in her eyes. Next view, the hair is brushed away again.
Visible crew/equipment: When Prancer is loose in the Riggs' house, he walks past and knocks down a television set. Right before he knocks it down, you can see the outline of the camera crew in the TV.