Do the Spanish speaking countries of South America have regional dialects?
I think that the many, diverse dialects in the UK make life more interesting.
Of course there are other dialects, remember that great part of South America was place of the Inca Empire in ancient tines, so our heritage still have the use of other languages like the "Quechua" (quichua) and Aymara that are not similar to Spanish, so they should be considered as other languages. In Peru, where the Inca Empire flourished and spread to other territories that now are part of Chile, Ecuador, Bolivia, Colombia and part of Argentina you still can see the same resemblance of race that was mixed later after the Spaniard Conquistadors came to these lands. They brought the Spanish language and part of their culture but many of our ancestors survived and they are still there with their own language and culture and in some places with the race intact. Within the Spanish language we can consider also as regional dialects the little differences within each country (North, South, West, East, Andean) and the more than little differences between all Latin American countries. I am learning those differences living in New York where I have the opportunity to meet Hispanic families on daily basis.
They certainly do. Not only from on country to another, but from one region within a country to another there can be marked differences in pronunciation and regionalisms.
Just like someone who learned to speak English in the US may feel utterly lost the first time he/she is confronted with a Scottish accent, so can a speaker from Argentina feel very confused the first time he/she tries to communicate with a fast-talking Mexican using lots of slang.