Factual error: Unless the regulations for the time period were different, the belt buckles seen with the regular fatigues is incorrect. They should be the same color as the belt and/or uniform. The brass buckles seen were used with the dress uniforms only. Also, any rank insignia worn by officers would have been dull in color so that they would be less of a target to snipers.
Continuity mistake: After Hawkeye and Trapper finish their toast to the Ritz Brothers, they toss their glasses over they shoulders. Trapper's flips in a lazy arc, and Hawkeye's in a flatter arc. When Radar is at the door, the glasses hit the door at a much higher speed and shatter.
Continuity mistake: When the General comes up, Pierce and Trapper are walking away toward the camera's left. When Pierce calls for the General's attention he is shown gesturing to the open door. Problem is, that they should be looking over their left, not right, shoulders, and we should see the inside, not outside, of the door.
Continuity mistake: After Klinger's file cabinet gets bombed, BJ appears in the window. He's facing directly ahead, head slightly tilted to the right. When the camera goes to a close up, he's in quarter profile, left cheek forward. In the long shot, he's back to the original position.
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: When Potter is on the phone, he turns to hush Hawkeye and BJ. As he does so, he's holding the receiver with his left hand, and covering the mouthpiece with his right. He then puts his left hand down on the arm of the chair. When the camera cuts in for a close up, his left hand is on the phone again.