Hawkeye mentions, for the fourth time since mid-Season One, having a sister. He also briefly mentions his mother. In later seasons, Hawkeye is an only child whose mother died when he was young.
After Klinger reads his "letter from home" to Col. Blake, Henry reaches around to get Klinger's file. When he turns back, he starts to open the folder. The camera angle then changes to over Henry's shoulder, and we see the folder is still closed and he proceeds to open it a second time.
When Radar and Frank are talking about the time difference between Korea and New York, the fact that New York is in the Eastern time zone would make the time difference 13 hours or 14 depending on Daylight Savings Time (DST). The 16 hours probably refers to the Pacific time zone (not in DST).
When Radar is explaining that "back home" is 16 hours earlier, Frank says that it's 5 in the afternoon here, and Radar says that means it's 1 in the morning yesterday. It would actually be 1 in the morning today.
When Radar takes down Frank's wire to his stock broker, Frank gives him a US currency one dollar bill instead of Army scrip.
Henry states he is 20,000 miles from home (Bloomington, IL); however, the true distance between Bloomington and Uijeongbu, South Korea is about 6,600 miles. Though it's very likely that Henry was exaggerating.
When Klinger talks to Henry in his office with his "letter from home", Henry reaches around and gets a folder with his previous "letters from home". But the letters Henry takes from the folder are not creased, so regardless of whether or not Klinger had faked them, they certainly would've been creased from being in an envelope, which the one that Klinger read was.
Trapper shows Hawkeye a photo of his daughters, but the photo is in 1970s-quality color, with the girls dressed in '70s styles and striking a "K-Mart Special" pose that was not used for portraits in the 1950s.
Hawkeye giving Frank a little "humiliation therapy" by tricking him into selling his recently doubled stock portfolio to invest in the fictitious Pioneer Aviation would do no long-term harm, because Frank's stockbrokers couldn't buy a stock that didn't exist. Thus, the money couldn't be lost. So, the worst that would happen is that his current portfolio is cashed out -- which he could buy back immediately at very close to the same price and lose only the cost of the broker's commission. He could even stand to gain a little if some of his portfolio went down a bit in the interim.