In a previous episode Hot Lips stated that her father was dead, now he is alive.
Early on in the series, Hawkeye repeatedly refers to Crabapple Cove as his parents' "summer home." In this episode however, he claims that his widower father (Hawkeye's mother was originally living, but by now that has long been changed by the writers) hasn't left the small Maine village in nearly 40 years.
In this episode, some letters to and from the families back home travel very quickly. In several previous episodes, it is noted that mail can take weeks, if not months to go back and forth.
Hawkeye's Dad addresses his letter "Dear Ben" even though he is the one who nicknamed his son, Hawkeye. More than once Hawkeye says he owes his nickname to his father's love of "Last of the Mohicans".
The party takes place near the end of March so presumably the members of the 4077th got the letters from their families within a week or so of the party. Yet when Radar talks to Major Winchester in the Swamp to make plans for his family to come out to Cape Cod to visit the Winchesters, crickets can be heard chirping in the background. Late March/early April would still see nighttime temps right around 32-40F (0-7C). Hardly the kind of temperature for crickets to be out and about.
When it switches between Potter/Klinger, Hawkeye/Margaret/Mulcahy, Winchester/Radar, etc reading their letters in the convoy of trucks, they're all actually in the same vehicle - the smudges and defects in the vehicles all match.
Klinger doesn't want his mother to know he's in Korea, which is why the camp makes up that Fort Dix facade, yet earlier in Season 4's "The Interview", Klinger says hi to his mother on TV, so she would already know where he was.