Nathaniel Fisher is Miles, the Radiation Controls Officer. He's a little hard to recognize because here he actually has hair, and it's brown, albeit noticeably thinning on top. He also has a mustache. If you are still asking Who Is This Guy Again?, he's the one who tells Lithgow that he has to report the missing plutonium. When they work to disarm the bomb, he's usually in the vicinity of John Mahoney (Frasier's dad).
According to IMDB, '80s teen pop star Debbie Gibson appears as an uncredited extra in this movie, about a year before she made it big in 1987.