Yes, I think that Spanish is quite similar in all these countries. Some differences are:

- The accent: It is quite similar in all South and Central America (except Argentina). In some words they pronounce the c-sound like the s-sound. For example: [Seresa] instead of [Zereza] (as it is pronounced in Spain) for Cereza. This is called "seseo" (because of the s) and it is admitted by the RAE.

- The grammar: no big differences in grammar except in Argentina. They use "voseo". This consists of using "vos" instead of "vosotros" (2nd person of plural, you) and they use a special verb form for this. For example they say: (you have, plural) "vos tenés" instead of "vosotros teneis". In some countries, they use "ustedes" instead of "ellos/ellas" (they) but they use the same verb forms. The difference here is that is Spain we use "usted/ustedes" to talk formally to somebody/people but in these countries they don't have this connotation of respect.

Anyway, I am not an expert at all about Spanish but I think that there are no very big differences (maybe the vocabulary).
I love listening to Argentinian people, they have a lovely accent, don't they? :D

See you!