In the scene where Hawkeye is taking pictures of the latrine, it's clear that the wideshots were taken outdoors at the ranch but the closeups of Radar and Trapper were shot indoors.
There are several times that Hawkeye's hair changes from shot to shot.
As Hawkeye tows the latrine away no holes are seen in the ground where the latrine once stood.
Hawkeye's camera was a Kodak Chevron. It was produced from 1953-1956. As such it was not available during the conflict which ended July 1953. Including the reference to Truman as President the presence of this model camera would have been impossible.