Goofs

At the end of the episode when Picard is in his dress uniform, he is not wearing any rank insignia which normally goes on the right shoulder just below the gold trim on those uniforms.

Bouncing a spacecraft off the atmosphere of a planet operates on the same principle as skipping a stone on the surface of a pond - in other words, it requires that the ship/stone approach the surface at an extremely shallow angle. The shuttle in this episode is seen to be pointing toward the planet at far too steep an angle to bounce off the atmosphere.

The shuttle does not cast a shadow on the Enterprise's hull.

The operations officer who bumps into Wesley in the testing facility has no rank insignia.

Towards the end of the episode when Picard is talking to Riker in the ready room Riker says the line, "You'll be able to shape the minds of the future leaders of Starfleet." The shot show Riker's reflection in the window but his mouth does not move.

Towards the end of the episode, we see Captain Picard run into Jake (a boy from earlier who had stolen a shuttle). The shot keeps going back and forth between them; you can see that the hallway curves to the right behind each of their shoulders', even as they face each other.

This would technically make the hallway an S curve - which isn't possible/likely, given that the ship is designed around a circular layout.

The crew informs Capt. Picard that the wayward shuttle is out of transporter range, but that simply isn't possible. If the Enterprise can use the transporter to transport people to and from the surface of the planet, how could it not be able to transport someone from a shuttle that is between the planet's atmosphere and the Enterprise?

Even if the shuttle were, for some reason, out of the transporter range, the Enterprise is much faster than any of its shuttles, so it could very easily maneuver into transporter range or, if the transporter isn't functional, into tractor-beam range.

It makes absolutely no sense that Capt. Picard doesn't immediately give the command to chase the shuttle once it is in danger. Maintaining a standard orbit in the face of this emergency serves no purpose.

When Remick asks Data if he is programmed to tell the whole truth, Data says, "Yes." This would be untrue. First he is seen over and over to not only withhold information, but from time to time has been seen to lie. Secondly, a being incapable of withholding information would be unsuitable in any kind of military organization, as they could never be trusted with sensitive information.