When he stabs himself in the leg with the scalpel, the way he pauses and looks at it sticking out of his leg, then attempts to casually put his other leg up to obscure it and act as if nothing is wrong.
The scene on the front steps of the castle with Frederick, Igor, Inga and Elizabeth. The entire filmcrew was laughing so hard they had trouble shooting it.
Frederick: Igor, help me with the bags.
Igor:Soitenly! You take the blond and I'll take the one in the toiban! RAWWWR...
On the DVD featurettes, you can see at least half a dozen failed takes of this scene where everyone cracks up.
Kemp:*Calmly* Wallowing in 'is grandfather's footschtops. Footschtops, footschtops!
"Blucher!" *WHINNY AND THUNDER*
Especially Eye-gor just popping out and shouting "Blucher" (*WHINNY*) to make the horses freak out, and Marty Feldman's impish grin.
In The Musical, the horses whinny when she just mouths her name.
Frederick tells the others not to let him out of the room while he's there alone with the monster, no matter what. Naturally, when the monster wakes up..
Frederick: Let me out, let me out of here, get me the hell out of here. What's the matter with you people?! I was joking! Don't you know a joke when you hear one?! HA-HA-HA-HA! Jesus Christ, get me out of here! Open this goddamn door or I'll kick your rotten heads in! Mommy!
'Y'know, I'll never forget my old dad. When these things would happen to him, the things he'd say to me..."
The best part of that is when he nods at the end, like it was a pearl of wisdom.
You know how funny this movie is? According to the commentary, Mel Brooks had to stick a handkerchief in his mouth when filming most of the scenes so he wouldn't ruin them by laughing from behind the camera. He had to do the same for the entire crew.
"Now, let us all go to my house for a little wine, a little spongecake- [the monster accidentally pulls Kemp's wooden arm off] Und shit! [regards his arm for a second, then points to the door with it] To the lumberyard!"