The term "Picard Maneuver" is used to describe a tactic of making a micro warp jump before firing weapons. Later, as a private joke among the cast, this term was used to refer informally to the way that Patrick Stewart's uniform shirt would constantly ride up and he would tug it back down.
The Stargazer was originally going to be a Constitution-class starship, like Kirk's Enterprise. The production team eventually decided they wanted to keep that ship special and not make it generic. The name Constellation class for the Stargazer was chosen because it could be easily re-dubbed over Geordi saying "Constitution class".
Director Rob Bowman on filming the scenes aboard the Stargazer, "It was just Patrick Stewart on stage, and when I shot first unit, I put a little compass, a degree meter, on the camera and got vertical, horizontal and lateral degrees, height of the camera, lens and so on. [Special FX supervisor] Robert Legato then would go back and do matching shots of the people in the chairs, over-expose them, put a number five fog filter on and transparent them about 50% on the screen so that they looked like ghosts. That was all done in post-production. It was kind of hairy, and as far as I know, I was the first person to use Steadicam on the show, which was fun. I try to use the Steadicam when I go on to other spaceships, just to give them a different feel from the Enterprise, that sense of uneasiness. But, working with Patrick was a real thrill."
A blooper from this episode exists on a gag reel included with the Blu-Ray season 1 disc set. On it, Brent Spiner, as Data, walks through the Stargazer bridge and upon seeing the dedication plaque, reads it using an imitation of James Stewart's voice and then saying "For God's sakes Mary, they built this thing in Bedford Falls!"
This episode marks the first time Wesley wears his rainbow-striped shirt, a costume he wears in every scene in which he appears for the rest of the season.