You will undoubtedly hear things in the DR that you will not hear other places and that you did not learn in any book or class. But, as with most idioms, they will be most often related to every day words. Things like 'pasola', 'motoconcho', and 'guinea'. But all grammar for all Spanish speakers comes straight from the Real Academia in Madrid, so it should be all the same, though some people's grammar is better than others, obviously, depending on the person.
Accents are accents, and everyone has a different one. If English was your second language you would probably have problems understanding a southern accent if you learned in New York or something. Once you get used to the Dominican accent you will be fine if you have a basic grasp of Spanish as it is.
I disagree that Castellano Madrile?o is very different from Latin American spanish. It is similar to the differences between British English and American English is my point of view. There are different terms for some things, and a very different accent, but you can understand each other. I have been taught by Latin American teachers in all my school years, but have had no problems in Madrid, besides noting the difference. I came to Madrid with a complete Dominican accent and was always understood. That is the beauty of Spanish... although Spanish was brought to the colonies hundreds of years ago, the language has been kept alive and all countries can understand each other!!
P.S. mommC: Italian is a horse of a different color. Italian chaos!! Provinical dialects are completely, and I mean completely, different from Classic Italian. Those that speak them are considered bilingual because in order for them to understand Italians from other provinces they have to switch completely to Classic Italian, the common language in the country.