The marching band repeatedly casts long shadows/no shadows between shots.
When the family arrives in Merrivale, one of the kids is suddenly wearing sunglasses when he wasn't in the previous scene.
When they are driving the road to Merrivale, the dad is driving the car, but when they arrive in Merrivale in the next scene, the mom is driving.
At Miss Goldfinch's house, while singing "What's Inside It?", Miss Goldfinch suddenly throws the egg into the air... even though it was on the other side of the room (and not in her hands) an instant before.
While at Miss Goldfinch's house, Barney and his young friends are astounded to see the magical egg move and wriggle. However, minutes before they'd already seen the egg move and wriggle back in the barn when they first found it.
When Baby Bop is in the barn asking where her blankie is, we can briefly see part of the actress' hair falling off from the costume.
David Joyner's ankle visible inside of the costume when Barney grabs Marcella's hand during the song "We Find A Way".
At the end of the "Old MacDonald" song, a guy can be seen waving his hands around when the animals are running.