Thinking Radar may be the father of a local's new born baby, visiting Dr. Sam Pak (played by Pat Morita) says to Henry: "You got trouble right here in pregnant city." This in reference to the the 1962 musical The Music Man. The Korean War went from 1950-1953.
Radar gets hit by a fresh egg while playing the bugle considering fresh eggs are meant to be pretty rare as mentioned on multiple occasions it would be a shame to waste it.
When the cow enters Colonel Blake's office, he tells Radar to "Get him out of here". Cows are female, not male.