Something the father said... (spoilers)
These are just two fun notions, not water-tight theories, nor would a good film put out a water-tight theory anyway...
In the beginning the father says that part of the solution for their children's asocial nature is to make a movie so that the family spends more time together. Could it be that the majority of the Home Movie it is a family-made horror film, and that all of them are in on it. It would certainly explain why everyone seems intent to keep the camera on and with them all the time.
Also there are a number of times when the characters mention that "it's the camera". Maybe it's the camera that is possessed and bringing out the worst in everyone -ignorant parents, evil kids- and perhaps even changing filmed events, such as two scenes which were rewinded and changed so as to have something spectacular to film. This would also explain why everyone is keeping the camera on and with them all the time. This could lead to a host of new explanations... since we wouldn't truly know which versions are true or not (as in Blairwitch Project 2).