The box holding the chess pieces falls to the ground but disappears in the closing shot.
Pieces teleport between squares all the time.
Geri moves the pawn in front of the King (White) as his first move. But when he places his glasses down to go to the other side, the pawn is in the original position.
(at around 2 mins) Black takes the White Queen, leaving just the White King on the board. The chess box is then shown overflowing with pieces, even though the only ones that have been taken are from White. Although this is less than half of the total pieces, there is no room for any others.
At the 2.24 mark there are two Geri's when in fact there should only be one. According to Jan Pinkava, this is an intentional joke.
When white Geri moves his king to the left, black Geri says that is illegal, but that is the only legal move that white can make. However, black Geri is just messing with white Geri in this instance. If he had truly believed the move wasn't legal, he would have already called mate.
"Nasty" Geri (black) moves a bishop illegally, two squares
horizontally to capture a pawn.