The ship identified as the USS Essex (CV-9) is actually the USS Yorktown (CV-10). The scene is from the Academy Award nominated short subject documentary film "Jet Carrier". The Yorktown is on public display in Charleston, SC.
In the episode, Trapper and Hawkeye mentions Capt. Forrest, one of the main characters in the M*A*S*H (1972) movie and novel.
When Radar places the call to Henry's home in Bloomington, Illinois he tells Lt. Col. Blake that he will only have two minutes to speak to his wife. The time from when Henry picks up the receiver until he loses the connection with Lorraine is in fact almost exactly two minutes.
We learn that Father Mulcahey has a sister who's a nun named Kathy
The banter between Trapper, Father Mulcahy, and Hawkeye in the mess tent is the typical back and forth from the opening minutes of the Jack Benny Radio Show. Father Mulcahy impersonates singer Dennis Day. In "The Winchester Tapes", Charles mentions the vocal similarities between Mulcahy and Day.