In the scene where Leito (David Belle) is being chased near the beginning of the film, the way in which he does it in is in fact an activity called Parkour and was invented by Belle himself, influenced by his father Raymond Belle. There weren't any special effects (wirework, computer graphics...) used in 90% of the Parkour scenes.
Despite common misunderstandings, the film is set in 2013 not 2010. The opening script on screen say that the sectioning off of District 13 was actioned in 2010 and as the camera surveys the wall you see markings that say "completed Oct 2010" in French. Then it says "Three years later" as the main film starts, making it 2013 and the sequel is 2016.
Several members of the gang in B13 wear American National Football League (NFL) jerseys from the New York Giants, New Orleans Saints, and the New York Jets. The production did not secure permission from the NFL Players Association to display any player's name, thus per the recommendation of the studio's lawyers, the names on the back were digitally removed before the film was released theatrically.
At the beginning of the movie, when K2 is looking for Leito and invaded the building, the two guards were watching a Brazilian soap opera called Por Amor, produced between 1997 and 1998. The scene they were watching is one of the most important of all soap opera (the actress Regina Duarte tells the actor Antônio Fagundes that she has changed the babies when they were born).
K2, also known as Mount Godwin-Austen, is the second highest mountain in the world, at 8,611 meters (5.35 miles), while the highest is Mount Everest at 8,848 meters (5.49 miles). In the movie, K2 is the second-in-command of the gang, and he's big, so the name fits.