I don't know whether it was the only show to parody the muppets, but there were plenty of refs to the muppets. For instance, the episode where peter loses his bones, becomes a superhero, and becomes a kid, there is one scene where Peter and Brian are watching a Count skit and Peter ever asks Brian if he ever killed a guy and drank his blood. Brian said that never happened.
I think I can help you...
#002: I Never Met the Dead Man
Stewie is outside playing with his Sesame Street phone, talking to Ernie(voieover heard. Not sure who did his voice, but I am guessing Seth McFarlane, the show's creator)
Stewie: Put me through to the Pentagon!
Ernie(on phone): Do you know what sound a cow makes?
Stewie: Don't toy with me Ernie! I've already dispatched with Mr. Hooper, I've got six armed men stationed outside Big Bird's nest, and as for Linda? Well, it's rather difficult for a deaf woman to hear an assassin approach, now is it?
Ernie: Can you count to three?
Stewie: Ho ho! Indeed I can!
(Stewie takes out a raygun and shoots the phone with it. At the same time he counts to three)
Stewie: One! Two! Three! (phone is now on fire) Can I count to three? For God's sake, I'm already shooting at a fifth grade level!
#004: Mind over Murder
Peter has been arrested in his own house after having punched a man(who actually turns out to be a woman)at a soccer game. A tracking device has been attached to his leg so that the FBI can monitor his every move. Peter is running around like crazy and tells Lois that he's so bored that he cannot watch TV anymore, as all the shows start running together.
And it cuts to a show entitled "Homicide: Life on Sesame Street", a parody of the crime drama "Homicide: Life on the Street" starring Ernie and Bert. Bert has brown hair shaped like a paintbrush, the same eyebrow, and voice is almost identical to Frank Oz's. Ernie has an oval nose and not as much spiky hair as he does. The announcer(Seth McFarlane)'s voicever says "This show contains adult content and is brought to you by the letter H"
Bert gets a phonecall regarding someone who's gotten his head blown off at Hooper's. He is also seen drinking.
Ernie: Bert, I wish you wouldn't drink so much, Bert.
Bert: Well Ernie, I wish you wouldn't eat(now getting furious)COOKIES IN THE (D word)BED!
Ernie: Bert, you're shouting again, Bert!
Skit ends with a comedic instrumental sounding like ones that would end every Ernie and Bert sketch. Bert makes annoyed grunt.
*Peter Peter, Caviar Eater: Peter wants to prove that Lois' aunt's house is historic. Here's the reference:
Peter: Wait wait! Come back! This is where the Pilgrims landed on Fraggle Rock!
*I am Peter, Hear me Roar: Lois and gloria Ironbox are fighting at a women's dinner party at a hotel. A chef walks out of the kitchen door holding banana cream pies(reference to Jim Henson's "Falling Baker" films on Sesame Street)
Chef: Ten banana-cream piieees!
(Chef gets run over by the two women fighting)
*A Picture is Worth a Thousand Bucks
-Peter asks the receptionist at a hotel: "Do you guys have bellhops that are rats, like the Muppets?"
-Meg, depressed that she has no talent, tries her birdcalls at Central Park(I think that's where it is. It is New York). Peter is impressed and asks her to do another one for him. She does, and after a short pause, Big Bird walks up to them acting like a tough guy. Big Bird is golden-yellow, has no feather-tops on his head, same color eyelids as his feathers, brown feet, and light/dark green-striped legs. He is voiced by Seth McFarlane
*Fifteen Minutes of Shame: Peter shows the cameraman his Madame puppet.
Cameraman walks away to see something more interesting. He wants him to come back because "she's gonna sing 'Rainbow Connection'!"
*Let's Go to The Hop: There's a new drug in town, and it is called Toad(basically licking frogs). Tom Tucker says it is also known as "lillypadding, Frenching the Prince, and Doing Kermit"
*Brian Does Hollywood: Stewie has a frog doll tied up and asks him if he's responsible for foiling his plans for world domination. The frog doesn't answer(since it's a doll!) Stewie threatens him by taking out a Miss Piggy doll and you know what he does with her.
*Fish out of Water: Tough biker wants tattoo artist to draw him a skull, but TA says he can do Kermit the Frog.
*Ready, Willing and Disabled: Peter goes to the TV station and demands commercial endorsements on a new TV movie starring Valerie BertandErnie(his mispronounciation of actress Valerie Bertinelli)
*Family Guy Viewer Mail #1: Super Griffins-Peter and Brian are watching The Count on TV, counting bats in his castle. Peter asks Brian if he's ever killed anyone. The Count looked right in the clip, but not sure who did his voice.
*Petarded-Hookers coming into the house and being counted(reference to counting bits on Sesame Street)
*Model Misbehavior:
Stewie has a conversation with Grover on the Sesame Street phone. The Sesame Street phone is different than the one in episode 2 because it has four buttons with very small detailed drawings(eyes are barely seen and so are several other details, but if you look at them, you will know who is who) of Big Bird, Ernie, Grover and The Count, and in the next scene, Grover is replaced by Oscar the Grouch. Big Bird is golden-yellow(w/o feathertops), Ernie has straight hair and red shirt, Grover has the same blue fur with red lip(and the nose is seen in the center of it), The Count has a black cape(yet his face can be barely seen), and Oscar has yellowish-green fur(almost the same color of urine) and small black eyebrows
*Cookie Monster is seen in rehab, and again lighting cookie dough on fire in the ladies' restroom at the Drunken Clam
*Jungle Love: Peter's flashback of when he used to work with Bunsen Honeydew
*The Father, the Son and the Holy Fonz: The Pinball/Stewie clip