As Mulcahy performs the tracheotomy, the sky is overcast. When he and Radar hop into the Jeep minutes later, the sky is sunny.
For plot convenience, this is the only installment in which a M*A*S*H jeep is seen equipped with a two-way radio. A radio would have come in quite handy in "The Yalu Brick Road" and "Hawkeye" in which jeeps overturned.
When Corporal Cupcake (the dog) is first seen, he's sitting on all fours, with Hunnicut leaning over him and Hawkeye approaching them, in the next shot Cupcake is lying on his side, with both Hunnicut and Hawkeye next to him.
Hawkeye calls what Fr. Mulchay did to the soldier a tracheostomy. The proper term is tracheotomy. The term "tracheotomy" refers to the procedure to make an incision (cut) into the trachea (windpipe). The opening itself is the "tracheostomy."
After Father Mulcahy makes the initial incision in the wounded soldier's neck and lifts his hands to say grace, his Tom Mix pocketknife is shiny and unbloodied.
The last artillery explosion during the tracheotomy is within 10 yards of Mulcahy and O'Reilly, well within killing range, or certainly close enough to severely wound all three.
When preparing for the trip to the aid station, Radar and Igor are both wearing cartridge belts but neither carries a rifle or wears a sidearm.
It wasn't proven that expired air was sufficient to maintain adequate oxygenation until 1954. And mouth to mouth resuscitation wasn't developed until 1956. The army didn't adopt it as policy until 1957. So B.J.'s mention of it is out of place.
In the early 1950's Mulcahys dropper tube would have been made of glass not plastic. The modern plastic Pipette wasn't available until 1957. So he wouldn't have been able to cut it.