This is the only appearance of Lt. Cmdr. Sarah MacDougal as Chief Engineer. After this episode, Lt. Cmdr. Argyle would be Chief Engineer, followed by Lt. Logan. Geordi took over the position when the second season commenced.
When Troi heads to Engineering, she refers to Riker as "Bill." This is the first time in the series anyone has called the second-in-command by that particular variation of his first name. Troi later calls him by it again in Star Trek: The Next Generation: Haven (1987).
George Takei said in his autobiography, To The Stars, that he thought this episode was a total copy of one of the best Star Trek (1966) original series episodes (Star Trek: The Naked Time (1966)), that it was unoriginal, and it was like seeing "young children putting on their parents' clothes and trying to act like grown-ups."
When Riker and Data are looking at the view-screen showing the Tsiolkovsky's bridge with the blown-out hatch, you can see a plaque just behind Data with the name of the ship written in Russian Cyrillic text. This is the only instance in any Star Trek series where the ship's name is displayed in a language other than English.
During the scan of the records, we quickly see a bird (Parrot) with a barely distinguishable human head (Gene Roddenberry's) on a perch wearing a Starfleet uniform, complete with insignia. This is a reference to Gene's fan inspired nickname, "The Great Bird Of The Galaxy."
A major plot point of this episode is Wesley's "invention" of a re-pulser beam which is treated as an ingenious idea. However in the original Trek episode Star Trek: Who Mourns for Adonais? (1967) when the Enterprise is being held in a force field, Kirk orders Sulu to modify their tractor beams to repel against the field. So Wesley's idea was not as out of the box as it appears to be.
The limerick that Data quotes, was written by Star Trek (1966) writer David Gerrold. The complete version of the limerick can be found in the third book of his War Against the Chtorr series: A Rage for Revenge.
The story went through various stages of wackiness in its early rewrites. At least one draft played it more seriously, using the polywater virus as an opportunity to explore the new characters and what makes them tick (as per Star Trek: The Naked Time (1966)), but the shooting script dropped most of this character background in favor of massive amounts of comedy instead.
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 Star Trek: The Next Generation: 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."