The filming location was right under the flight path of Van Nuys municipal airport, which meant that airplanes were constantly flying over the heads of the actors, and the entire scenes filmed there had to be re-dubbed in post production.
The Edo exteriors were filmed at the Tillman Water Reclamation Plant and Japanese Gardens in north Los Angeles, and the section with Wesley's fall at the Huntington Library in Pasadena. The Tillman Plant was used to represent Starfleet Academy and Starfleet Headquarters in later Star Trek episodes. It also served as Bill and Ted's University in Bill & Ted's Bogus Journey (1991).
Wil Wheaton cringes to this day over Wesley's "I'm with Starfleet, we don't lie" line, though admits that in retrospect it actually serves a purpose, showing that Wesley may be smart, but he's also extremely naive.
Gene Roddenberry apparently wanted the Edo to wear even less clothing, but the costume designer couldn't make it any skimpier without the risk of it falling off altogether.
This marks the first of three times the Captain shows a native woman her home planet from orbit. This happens again with Nuria in Who Watches the Watchers (1989) and Lilly in Star Trek: First Contact (1996). This approach clearly has meaning to the Captain as he tells Anij in Star Trek: Insurrection (1998), seeing his home planet from space for the first time was a moment where time stood still.