During one scene in Col. Potter's office, Col. Potter is spelling someone's name on the telephone. Hawkeye, standing nearby, responds by chanting "M-O-U-S-E" - part of the "Mickey Mouse Club" show's theme song. The "Mickey Mouse Club" did not debut on television until October 3, 1955, more than two years after the ceasefire that ended the fighting in Korea.
BJ's daughter Erin's age is constantly jumping back and forth. When he first arrives, he explains that he received his orders to report after returning home with his wife from their first night out after Erin was born. When Radar leaves, Erin is big enough to walk up to Radar and call him "Daddy." In the next season, BJ explains that on his last anniversary, Peg was still 8 months pregnant with Erin, which would make her less than 1 year old. A few episodes later, Erin is once again talking in full sentences and is nearly 2 years old.
In Harry Morgan's first season as Colonel Potter his only child is a son whose wife has a daughter. However, by the end of the series his only child has become a daughter and her husband visits Col Potter at the 4077.
Hawkeye's background and family situation changes quite a bit during the run of the series. At the beginning he is from Vermont, both parents are living, he has a married sister that sends him an oversized homemade sweater, and a nephew. By the end of the show, he is from Crabapple Cove, Maine, and he is an only child whose mother died when he was about 10.
Although the Korean war lasted slightly over than three years (Summer of 1950 through Summer of 1953), MASH seemed to pack at least four or five Christmases throughout its run. Of specific note: Dear Dad - 1972, Dear Sis - 1978, Death Takes a Holiday - 1980, Twas the Day After Christmas - 1981.
Several of the characters had multiple variations on their names during the series, perhaps none more so than Father Mulcahy. His name is given at various points as John, John P., Francis, Francis John Patrick, and John Patrick Francis
In the early seasons, Vietnam-like references were often made by characters: Claiming their location was in "Southeast Asia" (Korea is in northeastern Asia) and searching for missing colleagues in "the jungle" (there are no jungle regions in Korea).
As a rule in the service, a person is only awarded one Purple Heart (the first time they're wounded) and then oak leaf clusters for subsequent injuries. However, multiple characters throughout the series have or receive more than one purple heart.
Three different people have been named "Nurse Baker", including a single woman, a married woman and a woman of a different race (she was Black while the other two were Caucasian). However, Baker is a popular American name, and could have been shared by more than one person in the 501st.
Two sets of the camp were built, one in the outdoors, and one within a studio. This is apparent in numerous episodes when the characters are standing "outside" in broad daylight, but each cast member has numerous shadows as a result of studio lights shining in different directions, as well as an echo within the studio that is not audible on the outdoor set.