Luigi's repeated failed attempts at trying to run away from Sunnycide.
The "L33T HAMM3R BROZ."
The moment Toadsworth sees his past self with Baby Peach, he instantly assumes that his younger self has de-aged Peach into a baby and kidnapped her, and starts chasing him around. Even when he figures out the truth, he just can't get along with his past self. On a related note, their attempts to cheer Baby Peach up are also pretty funny. The Mario Bros even use these to learn new moves.
After falling into the secret caves under the Koopaseum, the babies attempt to wake up their unconscious adult selves. Baby Mario's solution (as usual) is to hit Luigi with his hammer. This does wake up Luigi, but he (understandably) gets mad at Baby Mario, which causes him to start crying. This causes Baby Luigi to start crying as well and Luigi starts panicking. Mario wakes up to the sound and he gets mad that Luigi made the babies cry. Which causes Luigi to start crying as well.
The Star Gate's insinuating that Luigi is not pure of heart and cannot go through him, dangling a certain "secret" of Luigi's that the Gate claims is scandalous. Also, it claims that Mario should really eat more healthily than he does.
If saving upon entering Gritzy Desert for the first time, the save file description reads as follows: