Margaret's father Colonel "Howitzer" Al Houlihan visits the 4077th, despite the fact that Margaret had earlier implied to Henry Blake that her father was dead.
When Margaret is saluting her father, Loretta Swit's fingernails are seen roughly an inch long. No nurse, especially a head nurse, would have fingernails that long.
After Al tells Margaret he is too tired to talk to her, he is in the officers club having a drink. However, it's possible and not even particularly unlikely that he was using "too tired" as an excuse to avoid the conversation, as opposed to actually being in the state he claimed to be in.
When the crate with the beef is opened, Klinger says that it's packed in dry ice. Real dry ice would be sublimating at room temperature giving off visible vapors, none of which is seen, revealing it's not real dry ice.