Should someone in his late 80s (with history of tias) have his carotids checked?

Absolutely. Someone who is having tias should most definitely have their carotids checked since the carotid arteries are the number one source for embolic strokes. In "symptomatic" patients, such as someone who is having tias, a carotid blockage of 50% or more warrants intervention.
You bet. Needs carotid doppler and possibly a cta of head and neck.