The character of Tom Paris was inspired by another Star Trek character, Cadet Nick Locarno from the Star Trek: The Next Generation: The First Duty (1992), who was also played by Robert Duncan McNeill. The creators decided they wanted a character "like" the cadet, and ended up with one who practically differed in name only. Ironically, McNeill was cast in the role as an afterthought.
This is the only episode in the history of Star Trek for which the hairstyling cost more than visual effects because most of the Janeway scenes had to be re-shot after the studio requested that Janeway have a different hairstyle.
Originally, Geneviève Bujold was cast as Captain Elizabeth Janeway, but she dropped the role after the first day of shooting because she claimed to not be able to handle the week-by-week shooting schedule of a show such as Star Trek.
It was planned for the EMH to be called Dr. Zimmerman. They later decided to keep the character named "The Doctor" throughout the run, however the creator of the EMH program was later named Dr. Lewis Zimmerman. Certain episodes from seasons 1-2 feature the name in the closed captions for the Doctor's part.
Even during auditions, the creative staff was unsure whether Janeway would be female or male. They opened up the auditions to both genders. Some of the male contenders for the role included Gary Graham and Nigel Havers.
The trivia items below may give away important plot points.
The following senior officers were killed when the Caretaker brought Voyager into the Delta Quadrant: Lieutenant Commander Cavit (First Officer), Lt. Stadi (Conn Officer), Dr. Fitzgerald (Chief Medical Officer) and his Vulcan nurse (T'Prenna), and the Chief Engineer.