The Summer Olympics was held in Helsinki July 19-August 3, 1952. However, during Season 4, it was noted that Col. Potter arrived to the 4077. Therefore, technically, Col. Potter would not have been assigned to the 4077 during the Summer of 1952.
In the final race scene Sgt Ames is seen approaching the pipe crawl. In the next close up he is exiting the pipe. He is never seen entering the pipe.
Hawkeye describes the marathon as "forty miles and no restrooms." A marathon is about twenty-six miles. It would have closer if Hawkeye had said forty kilometers, as a marathon is about forty-two kilometers.
After the scene with Margaret & Col. Potter in the office, when Hawkeye and BJ walk back into their tent it seems like BJ is stepping over something. Sgt. Ames comes in after exercising & collapses, falling forward. He then clearly bounces on the mat that was put down to break his fall.
As everyone sits in the mess tent during Potter's speech, the film set behind the tent cover is visible in the top left corner.
Potter uses a snub nosed Smith and Wesson Model 19 to start the crutch race, which turns into the stainless steel version, the Model 66, when he starts the partner race. The Model 19 was first available in 1956, while the Model 66 was introduced in 1972.
In the last scene, Sgt. Ames sees Hawkeye and BJ and calls to them, but his lips haven't moved yet when his voice is heard.