Other mistake: In the opening, the planet looks to be turning the same as Earth does. On the viewer it is turning correctly. However, it is too quickly to be accurate, assuming it is a copy of Earth. If so, at this higher speed, the days would be shorter. Also, the ship should be moving at such a speed as to see the planet moving in the opposite direction.
The Man Trap - S1-E2
Other mistake: When Crater is hit by the phaser, his collapse is sped up. (00:36:50)