My advice for tourists and residents alike, for the DR (and not just Santo Domingo)
#1 - NEVER drive around the DR with your doors unlocked. Papa Benito, why in the HECK would you let someone get into your car????
#2 - NEVER drive around with your windows down more than 2 inches. If they start trying to reach in and unlock your doors, drive off, with or without them hanging inside your window)
#3- if someone who looks like a cop motions you to stop, or to talk, stop somewhere in full public view, like right where you are, in the middle of traffic as long as you won't get hit from behind by fast moving traffic - force the guy to make a quick decision or get on with whatever he is doing (NEVER pull off onto a side street or somewhere dark) and either play like an ignorant tourist who doesn't speak Spanish, (and saying "me no speaky Spanish) or else say no more than "Que tal?".
#4 - just like a professional chauffeur, ALWAYS leave yourself an out, and a way to drive off if you feel physically threatened. Always have a way to turn out, and get away, even if it means the sidewalk, a side street, the median, whatever. Genuine tickets are preferable to physical harm to yourself or your family.
# 5 - have your paperwork in order, and easily accessible - the idea of a copy with everything on one page is a GREAT one. Give it to them if you must. (and here is a good reason to be like a dominican, and have an old address, or a wrong address, on your Dominican drivers license, if they were to get any cute ideas about showing up at your home later)