The danger is that a partial video or picture can be very misleading. I've personally seen cops get attacked by troubled people and it's not pretty. The attackers are disturbed and not rational, they do not obey commands to stop and keep violently flailing away at the officers. The cops have no choice but to use force to subdue the person for their own protection. Showing only the second half--which is what usually only gets filmed--is not accurate. Not all suspects are quiet and cooperative. (Our area had a suspected drunk driver in handcuffs still steal a cop's gun, kill him, and shoot other people in a hospital emergency room.)
Some police departments have placed cameras in police cars. They have captured motorists attacking a cop who pulled them over.
A second danger is such amateur videos could work in reverse and hurt innocent civilians. It could become a 1984 Big Brother situation.
Sadly, race politics played a role in this as well. Our local news had a video -- a full one from start to finish -- showing a cop clearly abusing a civilian bystander for no reason. But since they were the same race no one cared and nothing happened.