While riding in the sled which will transport him into the future, Jean-Claude Van Damme takes out a stick of Black Black chewing gum, a Japanese brand. During 1994, Van Damme appeared in television commercials for Black Black chewing gum in Japan.
Agent Walker always runs or is in fast motion (such as falling) when entering/exiting time. Senator McComb walks when entering/exiting time. This signifies that one has plenty of "time" and the other doesn't.
In the fight scenes in the last act of the film, Jean-Claude Van Damme's stunt double was used to create the illusion of the younger Max Walker. This was also done for Ron Silver's character of Senator McComb.
In the scenes where Jean-Claude Van Damme and Ron Silver are in their respective cars, the actors were shot on blue screen. The White House and D.C. backgrounds were added digitally in post-production.
The trivia item below may give away important plot points.
In the beginning, Melissa hears in the mall "Does Anybody Know What Time it Is?", by Chicago. Its lyrics has to do with a stranger asking for the time. She is again approached later by an unrecognizable (at first) Max.