Here are some bloopers I've found:
SS:
In the "Put Down the Duckie" special, when Phil Donahue interviews the Count, you can see Jerry's back. (Has anyone else noticed this?)
Towards the end of "J Friends", the top of a head is visible next to the female AM.
In the "Do the Alphabet" video, during the title song, you can clearly see the whole of an arm underneath Betty Lou's skirt.
TMS:
Liberace: During the Greek number ("Never on Sunday"), when the pigs, holding each other by the shouders as they dance, move up and down, I can swear there's a head next to one of them.
Harry Belafonte: When Kermit speaks in the intercom for Rowlf and Lew Zealand to come onstage, he calls Rowlf "Ralph". (George Burns also called Rowlf "Ralph", and so did Fozzie in the Rudolph Nureyev ep. Fozzie also called Rowlf "Ralph" in AMFC.)
Also in the Harry Belafonte ep., in the "Pigs in Space" scene, you can see Jim's headset and eyes under Link's costume and you can see some of Frank next to Piggy, too.
Gilda Radner: Towards the end of "Witch Doctor", just before the witchdoctor comes, Marvin Suggs' moustache and beard fly off when he pounds the Muppaphones.
Bob Hope: In the goodnights, the nose of one of the Zucchini Brothers (the blue one) becomes loose.
Marty Feldman: In the goodnights, you can see the arm of the puppeteer holding up the frog next to Marty.
Sylvester Stallone: During "Hawaiian War Chant", you can see Animal's sleeve.
Star Wars Cast: When everyone is on the planet Koozbane, and when Gonzo (as Dirth Nader) says there is only one weapon to stop Chewbacca, he is asked what it is, and Gonzo says, "Angus McGonagle, the Gargling Gargyle Gargoyle", instead of "Angus McGonagle, the Gargling ARGYLE Gargoyle".
TMM:
When Dr. Teeth says "Off the truck and on the job", an arm and head are visible.
During "Never Before and Never Again", when Kermit and Piggy are on a foggy street, a head follows Kermit.
TGMC:
During "Happiness Hotel", when Rizzo sings, you can see an arm underneath.
Also during "Happiness Hotel", when the Electric Mayhem starts playing, a head appears next to Zoot.
TMTM:
When Gonzo is backstage talking to the others about whether to do "Manhattan Melodies" on Broadway, you can see an arm and hand (holding the rod attached to his (Gonzo's) hand) underneath.
During "Saying Goodbye", when Scooter hugs Rowlf and Fozzie, you can see Richard Hunt's blue sleeve underneath him.
AMFC:
During "We Need a Little Christmas", when you see the rats and chickens, you can see the sleeve of one of the chickens.
Towards the end of "Jingle Bell Rock", since Bunsen, Beaker, Scooter, and Beauregard are watching the Electric Mayhem playing (with the rats dancing), Bunsen's glasses fly off and end up in the back of his head (since they are sewn to his head).
When Kermit is taking a phone call in the kitchen, the phone is still sewn to his hand.
During the carol-singing sequence, you can clearly see the sleeve of the Muppaphone.
BlueAM
"He's a lumberjack and he's okay,
He sleeps all night and he works all day."
SS:
In the "Put Down the Duckie" special, when Phil Donahue interviews the Count, you can see Jerry's back. (Has anyone else noticed this?)
Towards the end of "J Friends", the top of a head is visible next to the female AM.
In the "Do the Alphabet" video, during the title song, you can clearly see the whole of an arm underneath Betty Lou's skirt.
TMS:
Liberace: During the Greek number ("Never on Sunday"), when the pigs, holding each other by the shouders as they dance, move up and down, I can swear there's a head next to one of them.
Harry Belafonte: When Kermit speaks in the intercom for Rowlf and Lew Zealand to come onstage, he calls Rowlf "Ralph". (George Burns also called Rowlf "Ralph", and so did Fozzie in the Rudolph Nureyev ep. Fozzie also called Rowlf "Ralph" in AMFC.)
Also in the Harry Belafonte ep., in the "Pigs in Space" scene, you can see Jim's headset and eyes under Link's costume and you can see some of Frank next to Piggy, too.
Gilda Radner: Towards the end of "Witch Doctor", just before the witchdoctor comes, Marvin Suggs' moustache and beard fly off when he pounds the Muppaphones.
Bob Hope: In the goodnights, the nose of one of the Zucchini Brothers (the blue one) becomes loose.
Marty Feldman: In the goodnights, you can see the arm of the puppeteer holding up the frog next to Marty.
Sylvester Stallone: During "Hawaiian War Chant", you can see Animal's sleeve.
Star Wars Cast: When everyone is on the planet Koozbane, and when Gonzo (as Dirth Nader) says there is only one weapon to stop Chewbacca, he is asked what it is, and Gonzo says, "Angus McGonagle, the Gargling Gargyle Gargoyle", instead of "Angus McGonagle, the Gargling ARGYLE Gargoyle".
TMM:
When Dr. Teeth says "Off the truck and on the job", an arm and head are visible.
During "Never Before and Never Again", when Kermit and Piggy are on a foggy street, a head follows Kermit.
TGMC:
During "Happiness Hotel", when Rizzo sings, you can see an arm underneath.
Also during "Happiness Hotel", when the Electric Mayhem starts playing, a head appears next to Zoot.
TMTM:
When Gonzo is backstage talking to the others about whether to do "Manhattan Melodies" on Broadway, you can see an arm and hand (holding the rod attached to his (Gonzo's) hand) underneath.
During "Saying Goodbye", when Scooter hugs Rowlf and Fozzie, you can see Richard Hunt's blue sleeve underneath him.
AMFC:
During "We Need a Little Christmas", when you see the rats and chickens, you can see the sleeve of one of the chickens.
Towards the end of "Jingle Bell Rock", since Bunsen, Beaker, Scooter, and Beauregard are watching the Electric Mayhem playing (with the rats dancing), Bunsen's glasses fly off and end up in the back of his head (since they are sewn to his head).
When Kermit is taking a phone call in the kitchen, the phone is still sewn to his hand.
During the carol-singing sequence, you can clearly see the sleeve of the Muppaphone.
BlueAM
"He's a lumberjack and he's okay,
He sleeps all night and he works all day."