In one scene, Data tries leaning on the non-existent furniture after his conversation with Captain Picard about being fully functional and ends up falling on the floor. This was not in the script but was added by Brent Spiner on the set. Director Paul Lynch was pleased at Brent's idea and left it in the final cut.
Gene Roddenberry had hoped to recycle scripts from the original series with a bigger effects budget. Fan reaction to remakes (and a failure to achieve an early ratings peak) forced him to scrap plans to remake more episodes, at least as openly as in 'The Naked Now' which was a remake of The Naked Time (1966).
The Tsiolkovsky is named for Konstantin Tsiolkovsky (1857-1935), a Russian/Soviet rocket scientist and pioneer of the astronautics.
When the crew research the previous incident from The Naked Time (1966), the computer shows a diagram of the refit (film) ship, rather than the TV version. This was apparently deliberate, with the production team not wanting to show (what they considered to be) the now-dated look of the original TV series and would continue to do this until later on in Relics (1992), when the original Enterprise' bridge was shown, and more recently, the Blu-ray release changed the diagram to the TV version.
According to Wil Wheaton, Jonathan Frakes sharply criticized this episode, going so far as to calling it the worst episode he ever did, saying he felt "totally ashamed" by it. However, while recalling the first season (at a time near the end of the series), Frakes noted on how much greater the chances the writers took on the show than they did at the end of the series. In contrasting Skin Of Evil (1988), which he described as "absurd" and one of that season's "misses", he described this episode as "great" in as far as it being "the episode which we've never done anything quite like where everyone got drunk and horny. That was risky."