When Col. Flagg tells everyone to close their eyes so he could leave, you hear him running and then glass breaking as he jumps out the window. However the windows are made up of plastic sheets, not glass, and glass wouldn't be used in tents, or in a mobile unit near the front line.
Hawkeye is pretending to play for the Celtics and refers to the cheerleaders celebrating a good shot he has just made. However, the Boston Celtics have never had cheerleaders and only recently (2007) added a dance team.
Throughout the episode, Loretta Swit's fingernails are an inch long. Portraying a nurse, especially a head nurse, her fingernails should be much shorter.
Hawkeye and Colonel Flagg talk about the Sands hotel. Flagg says he used to be a showgirl at the Sands, which is unlikely because he was already in Korea by the time The Sands opened in December of 1952.
When Radar first asked Klinger about Maj. Houlihan, Klinger was half asleep and incoherent when he muttered the word "baby." But by the time Klinger was awake and moving about the camp, he would have heard that Maj. Houlihan was missing and reported to Col. Potter that she had left camp to deliver a baby.