I'm not knowledgeable enough about planes, trains, cars, guns, architecture, geography etc. to be bothered by those kinds of mistakes.

However, I do notice when someone is playing an instrument (especially if it's a stringed instrument) and their fingering and/or bowing/strumming has no discernible connection to the music you hear (Pa's fiddling on Little House on the Prairie comes to mind). Likewise dancing that is entirely out of rhythm with the music being played
(I particularly remember an episode of Hart to Hart where they attended a Highland Games; they showed a minute or so of sword dancing where they clearly had just put some bagpipe music into the soundtrack while the dancing was going on. It was at least the right music for the sword dance, but the dancing was completely out of sync
with the music.) That kind of thing really does bug me and strikes me as real sloppiness -- they don't even need to do any research to see/hear that these things don't
match up, but can't be bothered to get it right...