Continuity mistake: When the cops capture Killer Kane, the first cop to grab him loses his hat in the struggle. In the very next shot of him, just before the other cops arrive, he has his hat on again. While there might have been just enough time for him to put the hat on while the camera was not on him, he would have had to do so before handcuffing his prisoner - probably not a good idea.
Continuity mistake: When Kevin sleds down the hill, he flies through the air when he reaches the dead end and he crashes face first into a pile of snow. By the way he falls it seems he only fell a few feet because he did not hit the ground hard. But in reality, he was falling about ten feet.
Continuity mistake: When Max takes the garbage out and sees Freak over the fence for the first time, the first camera angle (looking straight down from above) shows that he is not wearing his headphones. However, the very next shot (looking at Max from the front) shows him removing his headphones. And yes, they are the kind with the shiny metal band that goes over the top of his head, so they should have been visible in both shots.