It is ALWAYS legal to film police in public. Taping private conversations when the individual doesn't know he is being taped is another matter.
No it's not. As many camera-phones now include audio, as you pointed out if it's recording audio as well it's not legal. Breaks Federal wiretapping laws. Straight video/pictures is legal but with provisions like you can't physically impede an officer in the process. You stand in their path doing it and it's not legal. Plus this is all Federal law. State laws might vary. As with other Federal-State legal issues, just because the Federal Law says one thing doesn't mean it's legal in every state.
Should be careful making absolute statements like "it's always legal to..."
Plus there's a difference between what's legal, and what's a good idea. Officer tells you to do something, unless you wanna spend you life savings in court asserting your rights, might wanna just obey the officer.