There have been a number of rulings [1] that have made laws restricting the filming of police doing their jobs unconstitutional. So that aspect of it is on pretty solid footing.

[1] An exemplar : http://www.infowars.com/supreme-court-upholds-right-to-film-...

It's usually just the audio portion that they argue about under "wire tapping" laws. The video portion is usually fine.

I thought all recordings (audio and video) are completely legal in public places because there is no expectation of privacy.

If I'm in a public place, I can record anything I can see from there.

No, no it isn't.

It may not be illegal but you still can get arrested.

http://www.infowars.com/illinois-citizens-still-being-arrest...