Other mistake: In the catacombs, Indy flips over the casket with the skeleton and dives underneath together with Elsa. If you watch closely, the skeleton gets trapped inside the casket, however Indy and Elsa are alone inside the casket. If the skeleton had sunken, there wasn't enough time, nor did Elsa or Indy bump into it when they dove underneath.
Other mistake: When Indy is atop the tank with his father, he is facing his father. Suddenly, they show a close-up of Indy's face, head-on, with the Nazi leader behind him swinging a shovel towards Indy's head in the background. Indy gasps, and ducks. How did Indy see the shovel being swung at his head if it was completely behind him?"