Factual error: When Hawkeye and Trapper arrive in Japan, as they approach the hospital in a Jeep, you can see a football field in the background. Look closely at the goalpost on the field. Instead of looking like an "H" (then in use), it is in the style used since the late 1960s: a bent single goalpost, a crossbar, and the uprights.
Factual error: Early in the movie, the loudspeaker announcer states that the Korean War was the #1 news item of 1951. Later in the movie it is announced that the night's movie is scheduled to be "The Glory Brigade" starring Victor Mature. However, that movie was released in May of 1953.