Continuity mistake: In the mess tent, Hawkeye is attempting to get the reporter to focus on BJ instead of him by telling the guy about the defibrillator made by BJ to save a life in the O.R. As Hawkeye is making his point, the reporter is putting a sheet of paper into a folder on his typewriter case. After the camera cuts to a close up of the reporter saying his next line, he's putting the paper into the folder again.
Audio problem: In the Post-Op ward, Jimmy is playing poker with the two jerks in his platoon. After the cards are dealt, he sees that their deck has pictures of nude women. He looks up at them when seeing this, and you hear him say "Very funny!", but his lips don't move.
Continuity mistake: As Hawkeye climbs under the table to hide there are three small stacks of white bandage boxes on the table. When the shelling starts, all the boxes in two of the stacks fall off the table, leaving one stack. When the shot changes, there are suddenly two stacks of boxes on the table.
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.