In the shooting script
The shooting script staged the hard hats as part of the team's cover story. Peter Venkman was to first wear a blue Con Edison hard hat while talking his way past the police, then swap it for a Nynex telephone company hard hat once the real Con Ed supervisor turned up. That Nynex hard hat was illustrated as white in the NOW Comics adaptation, but with the name misprinted as "NYEX."
In the finished film
On screen the Ghostbusters only ever wear yellow hard hats. Some were molded in other colors and painted yellow so the team would look consistent. Venkman's hat carries a "No Bozos" sticker above his right ear and a "100%" label at the back.
Egon Spengler's hard hat in the First Avenue digging scene has a sticker on the front that careful video analysis identifies as coming from a piece of airport equipment, a Runway Visual Range Remote Display Programmer. Two other small stickers above his ears are present but have not been deciphered.
In the same scene, Ray Stantz wears a stickerless hard hat with a battery-operated head lamp attached. He wears the same hat, or a very similar one, in the later tunnel scene, where Spengler and Winston Zeddemore also wear lamped hard hats.
Continuity and the brands used
Because the production used several different hard hats, close viewing reveals the style of a hat changing within a single scene. As many as seven different hard hats can be spotted across the film.
GBFans.com member David (Ramcuda) identified three of the brands. The only one Venkman wears is an ERB style 906. The one Spengler first wears is a Jackson Sentry Safety. The lamped hats worn by Stantz and Spengler in some scenes are Eastern Safety Tuf-E's with modified JustRite head lanterns screwed onto the front. Those two hats are visibly painted yellow over exposed white plastic, and the JustRite unit on Stantz's hat has a red plastic battery case.
Surviving props
At least two of the lamped hard hats have been displayed among original movie props. Both carry round "Ghostbusters 2" stickers that were applied sometime after filming rather than worn on screen.