Aid Station - S3-E19
Factual error: Mulcahy asks Hawkeye if he trusts God. Hawkeye replies "It says I should on all of my money." However, the phrase "IN GOD WE TRUST" didn't appear on American bills until 1957.
Aid Station - S3-E19
Visible crew/equipment: As Hawkeye walks into the Aid Station, the shadow of the camera plays across his entrance. Also, the area he walks through is extremely well lit, despite the fact the sun is behind the station, indicating stage lighting.
Aid Station - S3-E19
Other mistake: After Hawkeye gets back from Aid Station, Trapper is making a cup of tea. When he tries to hang the tea bag on a nail on the tent post, it unwinds and falls to the floor.
Suggested correction: This isn't a mistake, especially since we don't see it hanging back up in another continuous shot.
Aid Station - S3-E19
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.