I could name several segments that were clearly taped the same day as others -
From season 1 -
1 - Muppet Father & Son
2 - Professor Hastings' Y Lecture
3 - Kermit's What Happens Next Machine
4 - Letter F Story w/ Bob and Muppets
5 - Ernie's Cookie Reminder
6 - Ernie Prepares to Buy a Newspaper
7 - Ernie Dusts the Shelf
8 - AMs Cheer for the Letter F (all versions)
and, of course, Kermit's all-time classic hit song,
9 - "Bein' Green"
It's quite obvious that these segments were all taped the same day. First of all, they had aired within a course of two consecutive weeks, and were spread throughout those weeks worth of episodes (namely episodes 86-95).
As you can see, segments 1, 4, and 9 all employ the same forest backdrop/scenery. Kermit appears in two of those segments (4 and 9), so he was available that particular day for various inserts. The forest setting got good use in those three segments, and it just seems to be a rather appropriate setting for Kermit when singing "Bein' Green" for the first time. Could it be possible that this song was written way ahead of time, and the producers figured it would only be necessary to tape the segment whenever a forest scenery was available? Not specifically for Kermit's performance, but for at least two other inserts, as well. You may notice in the first version of "Bein' Green", the cardboard foreground of that forest setting was covered below the trees with artificial grass.
Jim and Frank, along with either John Lovelady or else Danny Seagren as assistants, were obviously all active on the set the day these segments were taped. That had conveniently allowed a certain number of segments to be taped with either Bert and Ernie, or else Kermit and another character.
You may also notice Professor Hastings has a green nose in the "Y Lecture" segment, the same as the father Muppet in segment 2, and the Fat Blue cheerleader in all variations of the "F Cheers" segments. Professor Hastings and the AM father are clearly the same puppet since they're both wearing a white dress shirt, red plaid vest, and grey pants. The only difference is their tie, hair, mustache, and eyes.
In the inserts with Bert and Ernie, the Ernie puppet bearing a raspberry-colored nose and donning an orange and magenta striped shirt is used, as opposed to the alternate puppet with a maroon nose and an orange and purple striped shirt.
Also, with the exception of the "Bein' Green" number, all of these segments seem to have a rather soft and subtle touch to the studio lighting. This is yet another indication that these segments were all taped the same day.