I am not sure if this counts but here goes...
For a while, the "Pigs in Space" sketch from the Harry Belafonte episode, the one with the "Dissolveatron" had puzzled me. It was not so much the sketch itself that puzzled me as much as it was the behind-the-scenes technicalities.
Normally, Link is performed by Jim, and Piggy is performed by Frank. But when the characters swapped bodies following their reappeance after Strangepork makes them dissapear with the Dissolveatron, I had always questioned this--at the moment that it is revealed that Link and Piggy swapped bodies, did Jim and Frank have to swap puppets? In other words, when Link is trapped in Piggy's body, did Jim have to operate the Piggy puppet with Link's voice and mannerisms? Did Frank have to operate the Link puppet?
On that same note, in regards to the Strangepork/Janice body swap, did Jerry and Richard have to swap puppets in a similar manner?
The only thing I understood was the Kermit/Swedish Chef body swap, and since both of those characters were Jim-performed, and Jim is already performing Link (still trapped inside Piggy's body), then that is self-explanatory, as I already know what had to be done if two or more characters voiced by the same performer had to speak in the same sketch.