In most of Argentina, Chile and Uruguay, people use a slightly different second person singular and corresponding present tense verb form. (vos instead of tu, and the conjugation differs: queres, tenes, etc. instead of quieres, tienes. Sorry about no accent marks but I’m on my home computer (a PC) and I have no idea how to make them. There should be accents on the last syllables of queres, tenes.)
LauraRae is correct saying that ll is pronounced zh in Argentina. Regarding being understood, I have an Argentine accent, but I have no trouble making myself understood by other Spanish speakers. It’s sort of like the difference between British English and American. The accent is different but understandable.
The one thing that is really different between Latin American dialects is that certain words have TOTALLY different meanings country to country.
Here’s an embarrassing example: in grad school, one of my good friends was Puerto Rican. One day I wanted to tell her how pleased I was with something, and I used the phrase “estoy chocha con [whatever it was]” and she just blanched. Turns out that’s a slang for female reproductive body part in PR. Whoops!
Many common words have many meanings, so you have to be careful. You don’t want to be throwing around phrases like “coger la guagua” which could mean “catch the bus” or “fuck the baby” depending on where you are.
And yes, you can definitely tell the difference between, say, a Mexican accent, a Cuban accent, a Puerto Rican accent, etc. In my opinion, the most difficult Spanish to understand is Cuban.