The Dominican Republic is not a particularly dangerous place to visit, but tourists should be aware of the following:
Perhaps the number one annoyance is not being given the proper change after a purchase. In many cases it is a legitimate error in math. But it's not entirely uncommon for waiters, taxi drivers and shop owners to 'accidentally' give you less than warranted. If something's missing, say so right away.
Buying drugs in the DR should be avoided. The seller is often in cahoots with the police who 'catch' the exchange in order to extract a bribe from unwary foreigners. Any transactions involving large amounts can result in significant prison time. Also worth noting is the reputedly 'impure' quality of the cocaine distributed in the DR – public service announcements warn that the majority is more dangerous chemical filler than anything else.
Prostitution is not illegal (brothel ownership and 'pimping' are) and is big business in the DR (Boca Chica and Sosúa have the highest visible presence). It is definitely illegal to have sex with anyone under the age of 18, even if the offender doesn’t know the prostitute’s real age. Female prostitutes, when propositioning foreigners, are known to grab and touch aggressively, often a sly attempt at pick-pocketing.