Belarusians are typically quite friendly to foreigners, sometimes too much, however. Some less scrupulous individuals intoxicate visitors to such a degree that it's easy to rob them. The best rule is to never accept a drink from a stranger but never refuse one from a trusted friend.
Western men are advised that attentive females encountered in dancing clubs and bars are highly likely to be con artists. The typical ploy is that after you take her to a private location, her large "boyfriend" emerges to accept your "apology" for toying with his girl. Your apology will come in the form of cash.
Registration is the single most important safety precaution. Admittedly, this is the means by which the government keeps track of the movement of foreigners under the guise of visitor safety. However, being caught with a registration older than three days can result in complicated situations. Hotel agents will automatically register when you check in. Registration for staying in a private residence, however, can be complicated and requires a long wait at a local office that can be exceedingly hard to find.
Police in Belarus are well-known for being closed-minded. Given the largely homogenous fashion sense of people in Belarus, wild aberrations in clothes or hairstyle may single you out for suspicion of possession of narcotics. Again, have that registration with you at all times.
