I love bloopers. Especially medical, military and historical. It does bug me when the male actor has pierced ears in an inappropriate era. Or, did bother me. I'm too blind for details now.
The film and TV people I've known do not care about these things. They have continuity people and the rest is que sera. I know of one producer who is actually a jerk about it but people do point out mistakes in his product often. Must be a drag.