Col. Potter states that he has an 8 year old granddaughter. In "Mail Call....Again", less than a year earlier, his first and only grandchild was born.
Throughout the series, it is always emphasized how scarce real eggs are, whereas the M*A*S*H personnel always have to make do with powdered eggs. It is thus very unlikely that BJ would waste any on a simple practical joke.
During Sidney's monologue about the patient he "lost," Frank's bed to his left is flat with obviously no one on it. After he says "that sweet innocent kid listened to the voices," a large lump is now on that bed that is then revealed to be Frank.
Klinger remarks that he would wear hula hoops for earrings if it would get him out of the Army. The modern hula hoop was invented in 1958, five years after the end of the Korean War.
Dr. Freedman writes that Father Mulcahy has "absolutely no training " as a therapist. A catholic priest is highly trained in not only theology, but how to relate to people.
In the aftermath of the overturned ambulance Hawkeye asks Capt Hathaway to assist him with the stretcher while Col. Potter asks Radar who the driver was. However, when they arrive in OR with the stretcher, Col. Potter is already scrubbed and performing surgery.
It seems odd that Frank wouldn't notice that many whole eggs in his helmet before putting it on his head.
When BJ tells Klinger he shouldn't wear hoop earrings, Klinger says he would wear hula hoops if it would get him out of the army. While hoops had been used for hundreds of years by various groups, the term hula hoop wasn't popular until the late 50s.
The supposed pilot, played by actor Charles Frank, is wearing the wings of a navigator, not the wings of an actual pilot or a bombardier. His dialogue in the episode lead you to believe that he is the pilot of a plane, or a bombardier, or a combination of the two which would mean he was either assigned to a multi-crew bomber, or a single occupant fighter. Based on the wings that he is wearing on his flight jacket, he is neither.
When Father Mulcahy is reasoning with the "Patient John," who refuses to get back in an ambulance or take a chopper, he tells the wounded soldier that he can be sent home by "a nice, slow, safe ship" and that John will see his family in about three or four months, after which John agrees readily to take an ambulance out of camp. But this is a faulty line of reasoning: Like all wounded, John would have to depart the 4077th by either ambulance or chopper; a ship obviously can't dock at the camp. Furthermore, as an enlisted man, John would be sent home from Korea by hospital ship anyway, so there's no avoiding these modes of transportation or the months-long trip home.