The Burgermeister falling down the stairs because of a toy duck. The choppiness of the animation is the best part of the gag: each of his limbs goes limp one after the other with a significant delay, all the while he has this slack-jawed, bug-eyed look of agony on his face.
The That Reminds Me of a Song that Jessica sings which is completely irrelevant to the plot, but is still funny because of the 1960's acid colors.
And the delightfully cheesy "animation" trick they used to let her look at her reflection in the water; the animators stuck a photograph of her at the bottom of the fountain. Which remains completely stationary even as she sings.
The Running Gag with people criticizing Kris' clothes. When it's brought up a second time, he responds with this: