The restaurant that the family eats at was, at one time, a real restaurant; a national chain diner called "Sambo's". It was located directly across the street from Southgate Shopping Center, as appears in the movie. Due to the controversial nature of the name and interior design, the diner (and entire chain) closed sometime in the late 70s/early 80s except for the original location in Santa Barbara, California, which to this day remains open in its original location. It remained an abandoned building for many years, until Tim Burton came to town to film "Edward Scissorhands". Burton's crew unboarded the doors and windows and redressed the interior to look like a working restaurant again.
When Edward goes to have his hands sharpened, the storefront was that of an actual hardware store called Crowder Brothers in Southgate Shopping Center. At the time of the filming, they did offer a sharpening service, and they did have a giant motorized Victorinox in the window.
Tim Burton had asked Robert Smith of The Cure to do the soundtrack and had even sent the script. Robert was busy recording 'Disintegration' at the time, and didn't know who Burton was, so passed up the opportunity, handing Danny Elfman the job.