Hawkeye asks Klinger to call the Commander of the 1st Marine Division. However, the officer he ends up talking with and dealing with as Pvt Van Liter's commander is a Lieutenant Colonel. The commander of a Marine Division is a Major General. A Lieutenant Colonel is typically the commander of a battalion, not a division.
When Major Charles Winchester calls to Klinger about his ironing he is listening to music on a phonograph record. When they zoom into the tone arm it is very clear that the needle is not in contact with the record. Without this contact the needle cannot read the audio off the record thus no sound should be heard.
In the 1950s, marriage to a foreign national by an American citizen conferred US citizenship on the spouse. Unless the wife had been accused of a crime sufficient to revoke the citizenship, Josh's mother would be in no danger of deportation.
When Potter puts Charles in command, he states that he is appointing Charles "Top Kick Pro Tem." Top kick is an informal term for a first sergeant.
Hawkeye answers the riddle, "What's black and white and read/red all over?" with "A newspaper, or a suntanned zebra." What he had in mind was a sunburned zebra.