If I purchase bitcoins via p2p, can I get some problems if the bitcoins I get were involved in some criminal activity ? If yes then how do I avoid such situation ?
Honestly speaking, it's hard to determine whether the bitcoins were previously used for illicit activities or not.
Most of the criminals/hackers use mixers to get away with the trace to their bitcoins and this makes it very very hard to figure out if those bitcoins were used for criminal activities or not.
So I think we as a regular user/trader/investor shouldn't be much concerned about the bitcoins we are holding.