Most of the time regional differences do not cause huge problems. A person from one region might sound a little odd, or overly formal to the ears of somebody from a different region, occasionally they might have to repeat themselves to be understood. Occasionally however, a perfectly inoccuous and common word in one region can be very offensive in another.
The most obvious example is the verb 'coger'. As a European who learnt the Spanish of Spain first, this is a common word meaning 'to take'. As such I shouldn't feel in the slightest bit uncomfortable writing it here. Phrases such as:-
coger el autobus = to catch the bus
¡cogelo! = take it!
cojo el tren = I take the train
are all perfectly common in Spain. In Argentina though, Spanish people quickly discover that 'coger' has quite a different meaning - one that I am not so comfortable discussing in a blog for a general audience. Because of this, the phrases above sound ridiculous or offensive in Argentina, and Argentinians have a perception that Spaniards are oversexed as they want to c***r everything - busses, trains, etc.