Cuban police are everywhere and they're usually very friendly – more likely to ask you for a date than a bribe. Corruption is a serious offense in Cuba, and typically no one wants to get mixed up in it. Getting caught out without identification is never good; carry some around just in case (a driver's license, a copy of your passport or a student ID card should be sufficient).
Drugs are prohibited in Cuba, though you may still get offered marijuana and cocaine on the streets of Havana. Penalties for buying, selling, holding or taking drugs are serious, and Cuba is making a concerted effort to treat demand and curtail supply; it is only the foolish traveler who partakes while on a Cuban vacation.