When I was walking in the Tokyo Railway Station, several non-uniformed policemen stopped me. At least they claimed they were. They showed me their badges, which looked like real, though I had no idea. I then showed them my British passport. They immediately walked away. They did not looked into my passport. I was not even sure they recognised it was a British passport.
Because I was using Japan Rail Pass, so I always carried my passport with me. What would happen if I could not produce any identification? Are foreigners supposed to carry identification while staying in Japan? Do Japanese policemen stop people quite often?