Vox mentions a "Time Machine" musical and starts singing a song with the lyrics "There's a place called tomorrow...". Such a musical and such a song do not exist, although its composer Andrew Lloyd Webber most certainly does.
Originally released for December 2001, the release was bumped to March 2002 because of a decision whether to remove a scene involving a meteor shower crippling New York. The filmmakers were concerned that such a scene may stir memories of the terrorist attack on the World Trade Center.
Vox (the librarian hologram played by Orlando Jones) was originally written to be a robot. Steven Spielberg, however, was creating A.I. Artificial Intelligence (2001) at the same time, and had a similarly-designed robot in his own film for every version of Vox the filmmakers could conceive. Production designer Oliver Scholl came up with the idea of a hologram.
"Filby" from The Time Machine (1960) appears as a florist. When Young picked out his costume, he found the same period shirt he wore in the earlier film, complete with his name written on the collar! (Source: DVD production notes)
When Vox explains Hartdegen's biography, he mentions "1869-1903" as his years of birth and death. Since then Hartdegen stands in the future, 1903 turns in the year of his missing. According with it, Hartdegen is 34 years old when he travels to the future. Pearce was just one year older at the point of the movie.
When Hartdegen talks with Vox about time travel, this last mentions three real Sci-Fi writers: Isaac Asimov, Harlan Ellison and H.G. Wells. Asimov wrote in 1955 "The End of the Eternity", about the time travel and the risks about to make changes in the past. Ellison wrote numerous scripts about sci-fi (including time travel) for TV series like The Outer Limits (1963) and Twilight Zone (1959). Wells wrote in 1894 "The Time Machine", the book which is based the movie.
When Hartdegen starts to travel to the future, this one watches three mannequins in a shop window and as their clothes change across the time. In The Time Machine (1960), George watches the change of clothes of a mannequin during his time travel.