This is Will Smith's first film in 3.5 years, since the release of Seven Pounds in December 2008. This is the longest he has gone without appearing in a movie since his film career started in 1993.
The previous film Men in Black II released the same year as Spider-Man. This film, the sequel, releases ten years later; the same year as the reboot The Amazing Spider-Man.
According to the trailer Agent J travels from 2012 to 1969, 43 years into the past. He wakes up and sees a young Agent K, played by Josh Brolin. Brolin is only 21 years and 5 months younger than Tommy Lee Jones, who plays the older Agent K.
On July 15, 1969 - the night before the Apollo 11 launch - the moon wasn't full as seen in the movie, but exactly the opposite: it was a crescent moon, the day before a new moon.
MIB 3 Trailer: