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Continuity: 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.
Continuity: 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.