At the beginning, during the initial car chase, watch out for the couple in the rickshaw that Short Round bumps into. The sailor's on the right, his girlfriend on the left. Next time they appear, they have magically switched positions.
How Many Whips Does He Have, Anyway?
After Indy hangs the soldier on the fan by his whip, he leaves, with the man still hanging by his whip. Later on, Indy pulls out his whip, but he left it on the ceiling fan!
Ceiling Fan Cooperates
In the scene where Indiana Jones fights with an assasin in this room, the ceiling fan is initially shown turned off. Indiana finally wins the struggle by lassoing his whip around the assasin's neck and then throwing up the other end to the ceiling fan. The ceiling fan (now rotating) takes up the end of the whip and lifts the assasin thereby strangling him.
Where'd She Get Those Shoes?
Near the end of the movie, right after they ride the coal cars through the tunnels, Indiana Jones and company stand at the edge of a cliff, while water released by the bad guy shoots by. Notice that the girl is bare foot. Then, moments later, they are on the bridge and she is now wearing shoes.