The guy who uploaded this trailer of Ron Howard's best film--well, it's this or Splash--apparently transferred it from his personal 16mm print; deep catalog 35mm prints from the studios are becoming so scarce, let alone 16mm ones, it's hard to believe they once struck 16mm trailers.
Soundtrack on the trailer features Burt Bacharach's eminently hummable "Night Shift" instrumental (the vocal version was performed by Quarterflash) and Al Jarreau's "Girls Know How."
Revisiting this one recently, I was reminded of what a treasure trove of gritty early '80s NYC footage we get here (it seems a few exteriors were filmed in L.A., however, and I think I spotted 'em all). Its New York street cred is bolstered by an appearance by the one and only, Joe Spinell, as, what else, a sleazy gentleman's club operator. During one of several Times Square drive-bys, we see a marquee boasting Sharky's Machine (putting at least some of the filming in very late '81 or early '82; Night Shift was released in Summer '82, while Sharky's was a Christmas '81 release).
UPDATE: Found a version of this trailer that appears to be sourced from an old VHS tape. During the age in which they still packaged their videos in large, clamshell boxes, WHV sometimes stuck trailers at the end of the tape, following the feature presentation: