http://photocinenews.com/2010/06/03/videotaping-law-enforcement-illegal-in-3-states/
Did you really not know about this? Similar laws are currently in several states' legislatures. The laws make it a crime to video tape an on duty police officer, even in a public place where there is no expectation of privacy.
Perhaps I've missed something, but I don't believe these laws specifically prohibit videotaping law enforcement. Instead, ethically-impaired prosecutors have abused existing wire tap laws to suppress video evidence. The argument is that these wire tap laws prohibit audio recording without the consent of all parties, and since video recordings include sound, they are therefore illegal wire taps.
It's a preposterous and corrupt argument, of course, but it has been used to successfully suppress evidence and harass citizens making recordings in public places. I don't believe any of these cases have made it to SCOTUS yet. I do believe I read of at least one conviction overturned in a district court, but I'm not certain.
(Note also that these laws vary widely by state, which muddies the topic considerably.)
Police are public servants. We pay them; they work for us. With the narrow exception of undercover officers, there is no reasonable justification for prohibiting recording as long as it is done without breaking other laws (e.g., trespassing). One would hope officers acting legally would embrace recordings since they document the officers' lawful behavior.
I saw a recent article suggesting one way to avoid such prosecution is to not record sound, just video. While that might get one off the hook legally, I doubt it will help in the heat of the moment. If the cop has decided he doesn't want you to record, he's not likely to listen calmly as you explain you're only capturing video and are therefore in the right.