When Klinger is brought into Col. Potter's office after his first escape attempt (dressed as an old Korean woman), the MP who brings Klinger to the office is played by M*A*S*H semi-regular actor Dennis Troy. However, during the jeep-stuffing scene -- which is occurring simultaneously in the compound (as Klinger is leaving Potter's office, Maj. Burns enters to complain about Hawkeye trying to set the jeep-stuffing record) -- Dennis Troy, playing his usual role as the extra, "Phil," is seen in the background as one of the camp onlookers.
Early in the show, it is said that Richard Nixon is vice president but later, it is mentioned that Harry Truman is president. Nixon didn't become vice president until Harry Truman left office, in the last months of the Korean War. That wouldn't be for another seven seasons, in Mash-time.
When Hawkeye reads a newspaper from BJ's package from home, he reads it as "Elizabeth Taylor married someone whose name begins with N.I." Than he assumes it meant "Nixon", claiming Richard Nixon was their Vice President. BJ then corrects him saying that Elizabeth married Nicky Hilton. Nixon (who would become VP under Eisenhower) didn't become VP until 1953 and Elizabeth Taylor married Nicky Hilton in 1950. (Although, since the newspaper was used as packing material, it could have been an old paper.)
When the surgeons are having a discussion in their tent, the camera pulls back far enough to reveal outside. If there were four walls on tent, that would not be possible.
Surgeons and nurses are using latex disposable gloves;these did not become available until the early 1970s.
When asked about his church going habits, Frank Burns says "it's a great place to kill an hour." In the film, and earlier in the series, Frank was something of a religious zealot.