I bought my daughter a 2013 Mazda3 with 80k miles. Had it checked by a local, independent mechanic. Car checked out as having no issues. What issues should I watch out for with this vehicle?
Well the 2010-2013 Mazda3 is pretty much a Ford.
It was built on the 2nd generation of the Ford C1 platform (along side with the 3rd gen Focus)
Unlike some products on this platform, the Mazda3 isn't too bad - overall decent, although no Toyota or Honda.
As far as specific issues, it's hard to think of much.
keep your oil engine clean, maintain transmission very frequently (20k-30k, if assessable replace filter too. most have 4 speed Ford trannies they mainly used on the European market, although the ones with the 5 speed share the same one was the Fusion) and you should be good to go.