When Kikuchiyo tries to prove his lineage with a scroll. As the senior members of the Seven examine it, you can see in the background one of the other members count on his fingers the years involved in Kikuchiyo's claim. He begins to laugh uproariously in quiet just before the readers realize that Kikuchiyo would have to be a child for his evidence on the scroll to make sense.
Kikuchiyo demonstrates his skill as a horse rider by riding behind some bushes... The horse comes gallops out alone with Kikuchiyo chasing it.
This becomes a Brick Joke, since Kikuchiyo has to ride that same horse to the Bandits' camp later, with the similar results.
Meta hilarity, as Toshiro Mifune is probably the finest swordsman and rider of all the actors, but is cast as the buffoon who can't ride. Apparently this was done on purpose to distract the audience away from Kyuzo's actor, who was not trained in riding but plays the finest warrior of the bunch.
Kambei breaking the tension before the final battle with the bandits by telling Katsushiro, who was discovered with one of the farmer's daughters the night before to "Fight bravely, for now you are a full fledged man!" causing both the farmers and the other samurai to laugh.
Although Katsushiro likely felt it was a case of Dude, Not Funny!, seeing as he was reluctant to begin with, and his finally hooking up with Shino resulted in her father, who was paranoid of just such a thing happening that he hacked her hair off, beat her while Katsushiro did nothing.
Kikuchiyo Dressing as the Enemy and having an idle chat with one of the gun-wielders before drawing his sword. The Oh Crap look on the bandit's face is what sells it, along with Kikuchiyo's gleeful laugh as he gives chase.