When Hatton (Ben Kingsley) receives his clients after their time safari, he likes to compare them with great explorers: Marco Polo, Columbus, Armstrong... and he also says "like Brubaker on Mars", remembering a future (past for him) conquest of the Red Planet. Brubaker was the name of the commander of the Mars expedition in the film Capricorn One (1977), also directed by Peter Hyams.
A video game based on the film was released for the Game Boy Advance. It also had been considerably delayed, and ended up coming out slightly before the film, in March 2005. It was an overhead shooter with some driving stages, and included support for co-op and deathmatch multiplayer via link cable. A third-person action-adventure shooter based on The Thing (2002) engine was being developed by Computer Artworks for BAM! Entertainment for the PlayStation 2 and Xbox, but ended up being cancelled. Its plot differed from that of the film: the changes in the course of evolution were not an accident, but acts of terrorism caused by a Luddite cult. The "present" time was also changed to 2038. The game was to have nine missions taking place in both the past and present. Real-life bands would have been hired to provide the music.
The trivia item below may give away important plot points.
The change in the time line is caused by a single butterfly. This probably alludes to the so called "butterfly effect" in which a small change in one state of a system can result in large differences in a later state.