When Hawkeye and BJ are leading the camp in calisthenics, BJ points out that Charles isn't doing the exercises by yelling, "You, in the woodwind section!" to which Charles replies, "Brass." This is probably an inside joke, as David Ogden Stiers, who plays Charles, is also an expert French Horn player, a brass instrument that is frequently mistaken for a woodwind instrument (possibly because the French Horn is normally part of a woodwind quintet).
The title and concept for this show is based on the 1952 Helsinki Olympics.
In this episode Donald , Margaret's husband , is played by Mike Henry for his one and only appearance. In their wedding back in the last episode of season 5 he is played by Beeson Carroll , also for his only appearance.
The team names for the 4077 MASH Olympics are "Hawkeye's Yellow Blackbirds," a humorously ironic name, as blackbirds by definition can't be yellow; and "BJ's Pink Elephants," a reference to those who drink to excess, which the characters on the show often do. A very popular stereotype at the time was that drunks and alcoholics are prone to hallucinations, and pink elephants are the most frequently cited such hallucination, as they are a particularly ridiculous and fantastical thing to imagine seeing.
Emil Zátopek of Czechoslovakia had won two gold medals in the 5000 m and 10,000 m races, as mentioned by Hawkeye. However, BJ would have won their bet, as Zátopek ended up winning the Olympic marathon (a distance he had never run before).