Sandra Bullock (Linda Schell) was actually in New York with her family and witnessed the second plane, United Airlines Flight 175, crashing into the World Trade Center's South Tower (September 11, 2001)
Max von Sydow turned down the role of Hal in Beginners (2010) (eventually taken by his co-star in Skyrim Christopher Plummer) in favor of playing a mute in this film. Both men were Oscar nominated for Best Supporting Actor for their performances and Plummer won.
At age 82, Max von Sydow was nominated for an Academy Award for Best Supporting Actor for this film, becoming the second oldest man to be nominated for a male acting Oscar. von Sydow was aged 82 years & 289 days whereas the record holder was Hal Holbrook aged 82 years & 339 days nominated in the same category for Into the Wild (2007), beating him by just 50 days.
The scenes involving the swing set was shot in a part of Central Park called Cherry Hill. There are no swing sets or any playground equipment in this section of the park - it was added for filming only and then removed.
Thomas Horn came to the attention of director Stephen Daldry when, at the age of 12, he won $31,800 on a "Kids Week" episode of the TV series Jeopardy! (1984) that aired July 8, 2010 (a date Thomas mentions at 00:44 in the special feature "Finding Oskar" on the Blu-ray disc).
Second film related to the September 11 terrorist attacks to be nominated for an Oscar. The first was United 93 (2006). Both films were nominated for two Academy Awards and neither film won one. World Trade Center (2006) was not Oscar nominated, neither were September 11 (2002) or the more loosely related 25th Hour (2002).
The trivia item below may give away important plot points.
In an early draft of the script the Renter finally speaks at the end. Max von Sydow was opposed to it, since he felt the movie was about Oskar and it wasn't necessary to know whether or not the Renter recovers his speech. He was pleased that it wasn't in the completed film.