Two of the arguments bandied about are: 1) police have an expectation of privacy, and 2) people trying to videotape can interfere with police (if they get too close, etc).
1) There is no expectation of privacy in a public place; 2) In the vast majority of the incidents where police arrest someone for video taping, the person is nowhere near close enough to consider the video taping interference. In one case where the person doing the video taping was close, the guy was wearing a helmet mounted camera when a plainclothes officer pulled him over with gun drawn. The video taping wasn't an issue until the motorcyclist posted the encounter on YouTube.