My mother was quietly in love with Colonel Klink -- I could never figure it out but she was always impressed by him and secretly fearing how he'd always get it at the end of each episode, one way or another. She never knew that Werner Klemperer's agreement with the producers and the writers of the show was that Klink was to never win -- he did come close a few times, only in the last few seconds of the show to have lost again.
Also -- Werner Klemperer sang his role -- "Hogannnn", "Gen-eral Burkhalter, how-very-nice-it-is-to see-youuuu" and so on, no doubt influenced by his father, the legendary conductor Otto Klemperer.
Also all the Nazi officers were played by those with a Jewish background, and many sad stories about all of their wartime experiences, notably John Banner, that I'll leave to others to elaborate on.
A couple of years after the show went off the air, the entire Stalag 13 set was used for one of those SS porn movies (forgotten the title)-- I've only ever seen the trailer (and that was enough) where the climax of the movie had the entire set being blown up -- very sad that it was destroyed for this lousy movie, probably by the mid 70s WWii movies were out of style.