One thing that I've noticed is that of all characters Beaker frequently seems to be a victim of full-frame cropping. Did Muppet Labs do the fullframe work?
For example, in The Great Muppet Caper, at the end of the Happiness Hotel song, he's cut from a few shots in full frame. During the "You've got every kind of critter, you've got every kind of pest..." line, Beaker starts to walk at the end of the screen, but in full frame he can't be seen. And in the big group shot at the end of the number, he's at the very left of the screen, which is cut out in full frame (interestingly, not many other characters seem to be cut in the full frame version of that shot. Rizzo is, and I think Slim Wilson from the Jugband is, but I don't think anyone else is). This is something I noticed since I was a child, noticing Bunsen was there but not Beaker.
And after the various Happiness Hotel residents find out about Kermit's date with "Lady Holiday", Beaker is shown talking to Scooter, but in full frame we only see Scooter there.
And in The Muppets Take Manhattan, when the musical starts, Bunsen and Beaker are shown in a cardoard taxi cab which enters the stage for a second before cutting to a different shot. In full frame you can't see that they are there (well after I first watched it in widescreen I watched the shot in full frame again and I think I might have saw Bunsen there in the full frame).