The potter from "Kokoro Odoru" does a number of crazy things to try and find inspiration, from taking a dance aerobics class to spinning records at a night club.
In the "Taiyō ga Moeteiru" stage, the giant mouse tries to distract Ichirou/Salary-Man by offering to exchange business cards. If you fail that section of the stage, Ichirou falls for it and gets sucker-punched while searching for his pockets; if you succeed, he does a Double Take and punches the giant mouse.
The end of that stage has a funny moment too, if you know Japanese (or look up the translations online). Ichirou begins walking away after the fight, and his daughter asks him where he's going now that he's so big. Ichirou's response? "To work, of course!" (Which can be interpreted two ways: Either he's such a dedicated employee that even when he's huge, work is still the most important thing to him... or he's going to get some SERIOUS stress-relief from his crappy job. Given how depressed he is at the beginning, and how happy he looks when he announces that, it's most likely the second thing.)
"One Night Carnival" concerns a violin player plagued by stomach complaints on the day of a big performance. Desperate, he gears up to call the Ouendan just like any other... except his stomach cramps are so bad that, instead of the usual "OUENDAAAAN!" scream, all that he manages is a weak, strained "Ouen...da...n...".
In the cutscene before "Believe" is unlocked, the Yuuhi Ouendan are in the middle of taking a walk in the rain when they see the leader of the Asahi Ouendan using their own umbrella to shelter a seemingly abandoned animal in an old orange box. It's a minor moment of heartwarming if you're seeing Shinta or Hayato smiling at a cat or Rin petting a rabbit. However, if you see this cutscene on Hard mode, you'll see Kaoru smiling softly...at the bear that you helped the woman in "Go My Way" kick out from the hot springs.
On that topic, glance the top screen during the second segment of "Go My Way" and witness Kaede wrestling said bear in action.
Elderly Momotarou's dentures popping out as he shouts for the Ouendan.
The openings for "Julia ni Shoshin" (aka the hairdressing level) on Easy to Hard Mode.
On Easy, Hajime takes off his hat to remind the players that he shaved his head.
On Normal, Ryuuta is combing his hair really intensely.
On Hard, Kai refuses to take off his hat and gives a Death Glare to the player.
The presence of plumbers suspiciously similar to the Mario Brothers in "Bambina". If you perform poorly during these segments, they even jump around with the accompanying sound effect!
Fail for the first time in a stage while playing on Easy, and the Ouendan's leader will appear, telling you to try again as the life bar refills and the song resumes. For the Yuuhi Ouendan, you also get treated to a shot of Kai scarfing down the pot of food, complete with sound effects!