Visible crew/equipment: In the scene when Kermit confronts Doc Hopper he comes walking out of the bar. If you look at the top of Kermit's legs when he walks out, two pair of hands can be seen moving the legs.
Continuity mistake: Kermit's ice cream in the fair scene changes colour.
Continuity mistake: In the scene where Kermit, Fozzie, and the gang are following Gonzo, who is floating from the helium balloons, Fozzie opens his door and looks up at Gonzo. When he comes back into the car after Kermit shouts at him to do so, the steering wheel comes loose from the dash and all the Muppets start yelling at him for being reckless. In the next shot of the interior, the steering wheel is back in place. I do feel maybe this was a blunder that was left in on purpose, because it was so funny the way all the puppeteers ad-libbed a reaction to what shouldn't have happened, but it fails in continuity because in the next shot the wheel is fine.
Other mistake: Whenever Fozzie is driving the Studebaker, the movements of the car don't correspond to the way he moves the steering wheel (he tends to crank it back and forth a lot).
Continuity mistake: When Kermit and Fozzie come round the corner and see the billboard with Kermit's face on it, you can see that there is nothing behind the billboard. Yet later when Doc Hopper and Max are leaving, Hopper's car is behind the billboard. The car slightly sticks out, so Kermit and Fozzie should have seen it.
Visible crew/equipment: When Kermit is on his bike and enters the site of the Doc Hopper's Frog Legs Restaurant, look closely at the bike. You can see the wires moving the pedals of the bike; attached to the handlebars and behind the seat. Try to look for it when he rides by the black truck.
Audio problem: Fozzie and Kermit are driving right towards Gonzo and Camillia. When Fozzie says, "Yeah, cute huh?" if you look in the mirror, his mouth doesn't move.
Audio problem: When Gonzo is flying over the countryside with the balloons, his mouth never moves during all his lines except "Ah this is the place to be. Whoopeeeeee!"
Plot hole: How did Professor Krassman get shocked into being a frog? The electronic device doesn't even touch his head.
Revealing mistake: As Kermit walks by the bus, the lower portion of fabric covering the operator's arm is visible.