I was walking to work one evening(well, to my public transportation stop), in full uniform, which is identical to the cops uniforms, when I was mugged. I couldn't believe it! Of all the people to mug, you think you wouldn't go after somebody who looks like a cop. Then again, it was daylight, so they may have sized me up and realized I'm just some EMT or security guard or Culligan man or something going to work.
Another time, walking home from work(again, from my public transportation stop), they(the dudes hanging out on the corner making sure all is well in the neighborhood) would yell out, 'UC! UC!' alerting other people within earshot that I was an under-cover cop. Obviously, this was just fine with me.
So, I guess it works both ways. I have the option of wearing a metal badge. I do not. It would inevitably get ripped off at some point and I'd be responsible for buying a new one, which is like $80 or something. Plus, I don't feel like pinning that on my shirt every day.
On duty, I'm mistaken for a cop quite a bit, but only by people who are drunk. It doesn't really matter. It's never been detrimental.