Assuming you have a UK passport - then no you don't need a visa. You fill in an entry card on the plane and hand it back when leaving.
I'm pretty sure (though not 100% - there are conflicting sources) that you need 6 months on your passport to visti Argentina - so yes it might be a problem
http://uk.visacentral...adCirRequirements.pdf seems to be the most authoritative source - it says 6 months.