This was the very first film to be given a PG-13 rating, but it was shelved for five months, making Red Dawn (1984) the first film to be *released* with the PG-13 rating.
The lead was originally offered to Matthew Broderick. When he dropped out, the character was rewritten for Matt Dillon.
When Mr. Brody (Richard Crenna) demonstrates a TV remote control to Jeff ('Matt Dillon'), one of the shows he channel-surfs to is The Real McCoys (1957). The scene includes Walter Brennan as Grampa McCoy and... Richard Crenna as Luke McCoy.
Marisa Tomei's first screen credit and contains her first spoken line of dialogue.
Cass Elliot of Mamas & Papas fame told producer Michael Phillips about Neil Marshall's script, which took over ten years to finally get made into a film.