Corrected entry: As Wesley and Picard prepare to depart the Enterprise, Data says the ship is at impulse speed. However when we see the shuttle exit, the ship is shown not to be moving.
Corrected entry: In the shuttle Picard picks up the plate of sandwiches with his left hand while holding a cup with the right. After Wesley takes a sandwich, the camera cuts back to Picard, who has the plate in his right hand, and no cup to be seen.
Correction: Picard never holds a plate of sandwiches and a cup. He has the plate of sandwiches in his left hand and a 2nd, empty plate in his right hand. He gives the empty plate to Wesley as Wesley takes a sandwich. Picard then transfers the plate of sandwiches to his other hand so he can take a sandwich with his left hand.
Correction: At impulse speeds, there would be no visible indication of movement as they're in open space.
This is incorrect. In-universe has shown the difference between a moving ship and stationary ship, even open space.
Bishop73
Exactly what is this difference you're referring to? If a ship is moving at sub-light speeds with only stars visible it is impossible to tell how fast it is moving, or even if it is moving. The only movement visible would be that imparted by the difference in movements of the camera and ship. (In fact, they create of the illusion of the ship speeding by by moving the camera past a stationary ship.) This is reality. If there is an error, it is the fact that the stars can be seen moving outside the hanger bay door which would indicate the ship was slowly rotating.