While Kermit the Frog is waiting for Miss Piggy to come back from the phone, time passes as indicated by the position of the moon rising in the background. The position of the stars should also change with the passage of time.
At the end of "I Hope That Somethin' Better Comes Along", when
Kermit the Frog and Rowlf harmonize on a final pair of long notes, they both hold the notes, audibly, until the end of the song, but Rowlf's mouth changes to a scat/improv line that he sings and we hear. (In other words, his voice is heard on two different musical lines at the same time).
Immediately after Kermit the Frog and Fozzie's first encounter with Doc Hopper, as Fozzie is driving away, Doc Hopper speaks several lines ("Hey, that's my car!", "I'm offering you money!"), but his mouth does not move.
When Fozzie and Kermit the Frog are about to confront Gonzo in his truck, Kermit says, "Fozzie look at that funny little truck!" in which Fozzie responds, "Yeah...cute, huh?" But if you look at the mirror in the car, you can clearly see that Fozzie's mouth remains closed.
At the end of "I'm Going to Go Back There Some Day", when Kermit the Frog leaves the group momentarily, Rowlf stops playing the harmonica for a few seconds, but we continue to hear the solo harmonica line.
When Fozzie gets Kermit the Frog's "Dragonfly Ripple" cone from the ice cream man, it's a shade of bright lime green. When he gives it to Kermit, it's gray. After the group spots Gonzo floating with the balloons the cone is green again, but a different shade.
When Kermit the Frog and friends first enter the front office of Lew Lord and speak to the secretary, the fan is already turned on in the background. However, Kermit then turns the fan on from the off position to spread the animal dander.
When Kermit the Frog goes into the El Sleezo café, he leaves his banjo outside. He does not retrieve it before getting into the Studebaker with Fozzie, but he somehow reacquires it when he plays and sings "Movin' Right Along" with Fozzie.
After Miss Piggy saves Kermit and talks on the phone to her manager, you see her hang up the phone. But, as she's standing by Kermit, and about to say goodbye, you can still see the phone receiver in her right hand at the bottom of the frame.
When Fozzie and Kermit the Frog are looking at the map, before they run off the road at the church, the road in the background makes two turns, but the steering wheel stays in basically the same position.