Factual error: After Radar asks Klinger when his home movies will be ready, Max answers, "Ready whenever you are, C.B." This is the specific punch line to a joke that relates to the actual filming of Cecil B. DeMille's 1956 movie The Ten Commandments, which wasn't released until after the Korean War.
Continuity mistake: When the Champ falls forward, he gets wine all over his sweater - you can see it when Potter and Hawkeye lift him. After the cut, his sweater is clean again. Considering the position of the stains relative to Hawk's hand, at least some stains would be visible.