When Henry and Radar are with Rosie, she shares the news that Janet Leigh and Tony Curtis have gotten married, which happened in June 1951. Later in the episode, Trapper and a patient discuss baseball player Ted Williams getting drafted, which didn't happen until January 1952.
When Henry and Radar and talking to Rosie, they determine that the dog that bit Radar wasn't eaten by the Korean couple because Radar's dog had a collar and tags and the dog eaten by the family didn't have tags. When Henry and Trapper are chasing Radar's dog, the dog doesn't have a collar or tags.
Usually, Frank wants to get any malingerers, goldbricks, and shell shocked soldiers back on the front lines immediately, instead of letting them get out of the war. This time, he wants Cpl. Travis transferred immediately to Tokyo.
To test an animal for rabies the animal needs to be put down first. Rabies can only be detected in the animal's brain. Two parts of the animal's brain need to be removed for the test.
In a scene where Colonel Blake has freshly vaccinated animals locked in cages two of the animals are a raccoon and skunk. Skunks are native to North and South America. Raccoons are native to North America. Neither animal is found in Korea in the wild.
When Margaret is reading a letter to Radar, her fingernails are over an inch long. No nurse, especially a head nurse, wold have fingernails that long.
We get another look at Radar's animal pen and it has animals that are native to North America and not found in Korea. For instance his raccoon and skunk.
Rosie tells Col. Blake and Radar that "Janet Leigh is marrying Tony Curtis" and "Ike's got the nomination all sewn up". Tony Curtis and Janet Leigh were married in June 1951 while Eisenhower didn't declare himself a Republican until January 1952 and didn't begin his campaign for the Presidential nomination until June.
Hawkeye refers to Godzilla, which did not exist until after the Korean War.
Bo Diddley's Diddy Wah Diddy was not released until 1956, three years after the Korean War ended.
When Margaret is reading the letter to Radar, she refers to Gogi Grant's "The Wayward Wind" as one of the letter writer's favorite tunes. The song, which was a #1 hit, was not released until 1956, three years after the end of the Korean War.
After Trapper tells Cpl. Travis that Ted Williams has been drafted and is "on his way to the R.O.K.," Travis, a Red Sox fan, laments, "Doesn't seem fair. He was having such a great year." But Williams played only 6 games for Boston before leaving the team to rejoin the Marine Corps, his last game being on April 30. And although he got off to a hot start to the 1952 season (a .400 average), 6 games can hardly be considered having "a great year," especially because he served as a pinch hitter in 4 of those 6 games. Furthermore, Williams' season was over so quickly that Travis probably never had the opportunity to even follow how Williams was faring before he was drafted back into service.