I always thought err was sort of short for error, so I pronounced it air.

I'm sure many feel that way. The AH dictionary has the etymology and a usage note (link). I have only heard the older pronunciation in the wild a couple of times from older folks who no doubt had it drilled into them long, long ago. Note, I am not suggestion that the older pronunciation is better or more correct, just that the newer pronunciation has nearly replaced it. I've never run across any normative grammarians/style-usagists who have insisted on the older pronunciation, because I think they are unaware that they are pronouncing it in the newer fashion, but it is fun to see that they are inconsistent in their peeves.

Ceci n'est pas un seing.