When Michael is dancing with the group of Russians, the amount of artificial snow on the floor keeps changing.
When Michael is dancing with the lady in the middle of the street, he holds a sheet from a newspaper. He then scrunches it into a ball and throws it away. It blows away, but then the newspaper suddenly appears right by his foot again, and is now flat and intact. Then in the next shot it has vanished again.
When Michael sings on the Statue of Liberty torch, he wears a sleeveless tank top and a white long-sleeved outer tee-shirt. In one shot the white tee-shirt is hanging down by his elbow so part of his arm is exposed, yet in the next shot the shirt is pulled up on his shoulder so the arm is no longer visible.