I had only one run-in with police in Moscow - they told me (through gestures since my Russian extends to numbers and "I don't understand it in Russian") I could photograph in the subway but not use a tripod. Overall I found the people very relaxed and friendly; I wouldn't worry about it at all.
Seriously, don't miss the subway.
I would love to do some urbex around there, but that is of course going to be (much?) higher risk.