Hawkeye tells Radar about how his mother died when he was a child and how his dad has been alone ever since. However, in #1.18 ("Dear Dad, Again"), Hawkeye closes a letter to his father with, "Kiss mom and sis."
Radar says that his mother's boyfriend "takes her over to Lockport for snow cones." There is no town in Iowa named Lockport. The nearest Lockport is in Illinois, more that 400 miles away.
BJ gives Radar a seven-digit number - 555-2657 - to dial Peg in Mill Valley. But US phone numbers in the 1950s were uniformly given as an exchange name followed by four or five numbers. Thus, BJ would have known his number as, for example, "KLondike-5-2-6-5-7," where the K and L in "Klondike" stand for the first two 5's in the phone number.
Radar mentions his mother's boyfriend's Nash Metropolitan. The Metropolitan wasn't introduced until 1954 - after the Korean War had ended.
At the end while in the Officer's Club a sign/shield is seen on the wall depicting the 4077th med co Air Ambulance with a helicopter. Assuming this is set in51/52 the helicopter shown bears no resemblance to any military assets in service at that time. The typical helicopter shown in the series is a Bell model 47. The one on the sign appears to be a much newer model like the Bell Jet Ranger.
When Klinger storms out of the movie tent, Col. Potter addresses him as "Radar."