I used to watch I Spy with my mom back in the day, she was a big Cosby fan (we owned all his records).
We had no idea that the shows were not shot overseas in the exotic locales represented but it's pretty easy to see which are the sound stage shots and which are the ones actually shot overseas.
The continuity and production problems are pretty well covered but they must have been a nightmare!
Imagine planning- "Okay for this episode they'll be wearing these clothes and we need a chase scene on a mountain in Hong Kong." and then keeping track of all the stuff they used for shooting back in L.A.
But they were able to fudge a lot of details because of the insular nature of American culture. We knew almost nothing about the rest of the world (many, if not most still don't) so they could get away with a lot that they would just not do today. Nothing to do with political correctness just massive inaccuracies.