All I can think of is double check for wear and rips in the lining and spots and extra wide lapels and patterns that are super ugly to you or match nothing in your closet. Those are crappy. But the thing about HT I love is that those tight weaves make for seemingly indestructable coats that look fantastic once they come back from the dry cleaners....some even without.
Non-Harris Tweeds are a crapshoot, but even those...a lot are nice. I just see so much Tweed and HT in particular up here in New England that I skip non-HT (unless it's Polo or something exotic for flippage).
By "crappy" I mean "poor quality," and I'm also a hard sell on tweed that isn't HT. Wide lapels are deal killers, but I don't worry too much about the liner if I like the weave. Presuming you pay $5 or less, they're pretty reliable flips, even ones by Stafford.