I expect a belayer to know how to tie the knot and what a proper figure-8 looks like.

Ok. I was picturing something where climbers were connecting to the belay with a carabiner and I was very o_O. I agree with you here.

it's relatively easy to miss things like an unbuckled harness or an unfinished knot

I can see your point. I'm even more safety conscious with the auto-belay (and I'm one of the most safety conscious climbers I've ever seen) but I could certainly see safety being an issue with newer climbers using the auto-belay.