Many of the cars already have dashboard cams. Some PDs also have wireless microphones that the cops wear and the audio is transmitted back to the car. I think it might be helpful to have 360 degree cameras in the in the back window, one on each of the sides, as well as an internal camera watching the backseat.
Then encounters could be fully edited together, even if someone says they were "assaulted" in the backseat. They could run nonstop and just be stored on a solid-state device which is backed up every 24 hrs to a central computer at HQ and kept for a certain number of years. Gun cameras aren't a terrible idea, so long as they remain a piece of the evidence and don't become something that dominates.

This isn't just all for liability. It's also really helpful for identifying suspects. Consider if a LEO away from their car is involved in a shooting, but gets injured or killed themselves. The suspect may have gotten away, but the LEO's gun may well have video of the suspect firing back at the officer. There's no question who killed the officer, and then the prosecutor doesn't have to settle for a reduced charge.

I've heard of proposals for devices on manned urban combat military vehicles that would simply be a cluster of very high-quality webcams that beam live footage back to a control area where people (in safety) can watch for threats and alert the crew. "3 o'clock - guy on a roof with an RPG" or "Grenade to your rear!" There's no such thing as too many eyeballs.