Factual error: After Radar asks Klinger when his home movies will be ready, Max answers, "Ready whenever you are, C.B." This is the specific punch line to a joke that relates to the actual filming of Cecil B. DeMille's 1956 movie The Ten Commandments, which wasn't released until after the Korean War.
Factual error: Klinger says he would wear Hula Hoops(R) in his ears if it would get him a discharge. For several reasons, he is using a phrase that does not yet exist:1) Show wise, Klinger will later try to convince Charles to invest in developing a new toy, a hoola hoop like plastic tube, being inspired by Korean children playing, and 2) plastic hoops which came to be called Hula Hoops were only introduced by Whamo in 1958. Setting episode dates is always difficult for MASH, but the Mash Olympics (inspired by the 52 Helsinki games) are still to come so we can say it must be 52. 3) The Hula Hoop trademark was only registered in 1962 to Whamo. No info. as to what name the hoops were marketed under prior to 62, but Klinger is using a term at probably ten years, at least 6 years, before it came into use.
Other mistake: Hawkeye, Henry and Trapper are playing scrabble. The board is in an illegal state - in the lower right corner 'it', 'jot', 'joy' 'yearn' and 'in' are not connected to the rest of the words. Since the others call Hawkeye on his non-existant word, I'm assuming they're playing properly.
Deliberate mistake: When Flagg turns out the light to escape.To make that effect they had to freeze a frame and then start again. If you look closely after Flagg turns out the light you can see Hawkeye and the Korean Man on the far right freeze. Then it shows Potter ordering the light back on.
Continuity mistake: In one of the earlier episodes Henry becomes the father of a baby boy; his other two children have been established as Molly and Janey, both girls. In "Abyssinia Henry," Henry get his discharge papers and wanted to call home with the good news. He tells Radar that he will have to wait a while, as his son, Andrew, will be practising his trombone. As Henry only has one son, Andrew has to be the son who was born while Henry was in Korea. Even if Henry was in Korea from the very first days of the war, by the time he left his son can't be any older than 18 months - hardly likely to be playing a trombone.
Continuity mistake: When the chopper carrying the soldier with the wounded back takes off, the sky is cloudy and, even accounting for the poor quality of the film, the weather looks very dull. The shot changes to show Radar, Hawkeye and Margaret watching the chopper leave and it is now bright sunshine.