Major Houlihan tries to contact her husband at the "2nd Army" in Tokyo. The Second United States Army was a World War I and World War II formation and was not in Korea.
The green trash can Margaret dumps and puts over Radar's head is a mold injection polyethylene 5 gallon bucket not invented until many years after the Korean war.
When General Fox points to the star on his shoulder and asks Hawkeye, "What does this mean to you?" Hawkeye responds by quoting a famous Texaco advertisement rhyme, "Always trust your car to the man who wears a star." However, Texaco did not introduce this advertisement jingle until 1962, 9 years after the Korean War ended.
B.J. claims that Bardonaro played a practical joke at BJ's wedding and that they both gave up practical joking "ten years ago" (Presumably after they both graduated from Medical School and after BJ's wedding). 1953-10=1943-both BJ and Bardonaro would have been drafted in World War II; yet Bardonaro wears only Korean War medals on his dress jacket. A further goof is that in "Welcome to Korea" BJ's age is given as 28-which means BJ went to Medical School at 14 and graduated at 18.