The sound of the door opening for Picard's ready room is not heard in an early scene with Data and the captain. Apparently Brent Spiner (Data) was standing just outside of the shot and walked into it.
After Riker and his team are overwhelmed in the Prime Minister's office, he is rendered unconscious by a phaser set on stun. But when he is being dragged away, you can see Jonathan look up at the camera as he thinks he is already out of the shot.
Pulaski scans a clone on the planet and without looking at any of her medical instruments is able to know that all of the people on the planet are clones.
When Pulaski scans herself for missing cells, she points the tricorder the wrong way.
The only episode where Geordi can tell when a human is lying. Humans lie in his presence countless other times and he never notices.
The episode's working title was "Send in the Clones."