Liam Neeson expected the film to bomb, but he signed on, in order spend four months in Paris, and learn karate, while playing the kind of role he had rarely been offered in the past. Ironically, not only was the film a massive hit, but created a new on-screen image for Neeson, as an action hero.
Jeff Bridges was first cast as Bryan Mills, but after he dropped out of the project Liam Neeson accepted the part, desiring to play a more physically demanding role than he was used to. Bridges eventually saw the film, and said Neeson was a much better choice for the role.
The map that Bryan is holding, when he finds out about the girls' plans at the airport at the beginning of the movie, is an old Europe map (probably dated 1992), as the now dissolved Czechoslovakia and Yugoslavia can clearly be seen. Czechoslovakia separated into two independent countries, Czech Republic and Slovak Republic, in 1993. Yugoslavia was dissolved in 1992.
Liam Neeson has stated in interviews that the biggest misunderstanding that people seem to take from the movie is that Europe (and France in particular) is a place where young people are at high risk of being abducted by human traffickers. He has said that several American parents thanked him after the movie for warning them of the dangers, saying they would no longer allow their children to go an a trip to France. Neeson always takes time to explain that the dangers were highly exaggerated for the film, and tells parents that they should encourage their children to get out of the USA more often.
Near the end, Bryan jumps off of the "Pont des Arts," a pedestrian-only bridge in Paris. In the scene, the bridge is unoccupied. In reality this bridge is a popular spot where people socialize, drink wine, and play guitar.