In early installments a camp library and librarian were mentioned, both would have come in handy had they still existed.
When the supply truck pulls into the 4077 you can hear the horn being sounded but the driver isn't pressing the horn he is steering the vehicle,
Charles nearly kills a patient when he mistakes curare for morphine in Post-Op. Curare was never approved for use in Korea, so it should not be there in the first place, and even if it was there, curare is a paralytic used in conjunction with anesthetics - it has no use in Post-Op.
When B.J. is talking on the phone to Abigail Porterfield, the author of "The Rooster Crowed at Midnight," he tells her that he never met Dr. Sun Yat-sen because the doctor died "over 30 years ago." However, Sun Yat-sen died in March 1925, and given that it's winter at the 4077th, the latest in the war that the date could be is the winter of 1952-53, meaning that Sun Yat-sen had died, at the most, 28 years ago, not "more than 30 years ago."
After Winchester accidentally doses his patient with curare, Hawkeye uses an Ambu bag to resuscitate him. Ambu bags were invented in 1953 in Europe, not released to the market until 1956, and certainly would not have been available in wartime Korea. The Ambu bag used in the episode appears to be a 1970s version.
The wounded soldier Charles gave curare to stated to Hawkeye he followed a set of footsteps in the snow to avoid mines until the footsteps disappeared. Instead of going forward into danger, all he had to do was reverse course and follow his own footsteps out to safety.