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.
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.
Marisa Tomei's first screen credit and contains her first spoken line of dialogue.