The scene near the end of the film, when all the children storm the castle and capture the evil Baron, the Baroness annnd the Child Catcher.
"Me Old Bamboo". Dick Van Dyke was 44 when he did that dancing, and it damn near killed him, but it looks awesome.
"Doll On A Music Box." Sally Ann Howes does such an amazing job at moving like a rigid mechanical doll that it's no wonder the court was fooled. Oh, also, she does it twice in a row. And she only needed ONE take. She claimed that the choreography was quite difficult, and doubtless she rehearsed a lot, given that she's said she wasn't much of a dancer, but she remembers the scene with well-deserved pride and fondness.
Dick Van Dyke deserves some credit for his floppy puppet act, too.