The best gag is not the famous clock scene, but when they hide from the landlady by getting into their coats and hanging themselves on the coat-rack.
Credit to Ed Park for noting that the literal high-point of this film is when Harold actually becomes a substitute for the American flag:
[…] the “typical American boy” turns into a parody of the Stars and Stripes—a flag, perhaps, commemorating all those who never succeeded in climbing their way to the top.