However, Wikipedia [1] implies this is not civil, but in regards to the government's view of privacy to you, not yours to the government, and is highly unlikely to supersede areas where filming is expressly forbidden, and which is indicated to you when entering that area.
[1] http://en.wikipedia.org/wiki/Reasonable_expectation_of_priva...
In Illinois and other two party notification states, you can't record audio of police officers in public places [1]. Video is fine, but since all video cameras record audio, it's a bit of a Catch-22. People get arrested all the time in two party notification states for video taping law enforcement and it's because of the audio function of their device.
[1] http://www.aclu-il.org/featured/2010/Complaint-ACLUvAlvarez....