The circumcision instructions are supposedly being relayed from a chaplain on the USS Essex (CV-9) but the ship shown, accompanied by Morse Code sounds, is the USS Yorktown (CV-10).
When Father Mulcahy signals to Hawkeye to begin the circumcision, the finger he points with changes from his left to his right between shots.
Hawkeye states that Captain Forrest has been gone over 2 years the Korean war only lasted 3 years in real time so everything that happened after this was less than 1 year,
When searching for a Rabbi to officiate the Bris, Father Mulcahy tells Radar to "try the Navy, try the Marines ". The Marines don't have a Chaplain Corps. Navy chaplains handle all religious activities for the Marine Corps.
The ship shown is CV-10 USS Yorktown not the CV-9 USS Essex like the story says.
During the bris ceremony, shots of an aircraft carrier - identified as the USS Essex (CV-9) but actually the USS Yorktown (CV-10), where the Rabbi is transmitting the instruction for the bris to the 4077th - are shown. In one of these shots, a Boeing Vertol Sea Knight (either a USMC CH-46 or Navy UH-46) helicopter is seen flying near the carrier. The Vertol took its maiden flight in 1958, and began to enter USMC/Naval service as the Sea Knight in late1964 - well after the "end" of the Korean War.
When Radar delivers the reel to reel movies to Colonel Blake, there are electrical towers visible on the tops of the hills in the background.