This show was fairly controversial at the time it aired, it wasn't liked by either UFO enthusiasts or the USAF. Not only did the program depict USAF investigators/investigations of UFOs to be too fair and even handed for those who believed the Air Force was conducting a UFO cover-up, but the true purists also disliked the liberties the producers took with classic UFO cases on which individual episodes were based. Some of the most famous cases of early ufology, such as the Mantell case of 1948, were butchered by the producers' decision to "update" incidents as if they occurred and were investigated in the (then real time) late 1970s. To an airplane guy, retelling (sort of) the Mantell incident with an F-106 in place of a P-51 was near sacrilege.
If you watch the opening and closing credits of the show, you'll notice the producers did not thank or even acknowledge the USAF for their assistance. It's my understanding the USAF did not assist the producers of the program, although a lot of stock footage of WPAFB and USAF aircraft were used. If other bases were involved in an episode, the bases were given fictitious names. The Air Force did not like the fact the show put them back in the UFO business nearly a decade after Blue Book was shut down. While I don't recall specifics, I do remember the USAF received an increased number of unwanted sighting reports during the show's two year run. I think the same thing happened during the early years of "X Files".
As others noted, the executive producer of the show was Jack Webb. Anyone who grew up watching Dragnet/Adam 12/Emergency would have instantly recognized the Webb formulaic approach to the show, complete with attempts at deadpan humor and reasonable accuracy in depicting the series' characters doing their jobs. Also noticeable were many of the actors who formed Webb's repertory company and played multiple roles across his various series. One casting quirk was that of Edward Winter in a lead role as the courteous, level headed officer (captain) in charge of Blue Book for the show's second season. At the time Winter had a reoccurring role on "MASH" as the paranoid, over-the-top intelligence officer, Colonel Flagg! I did find it odd "Project UFO" received almost no mention in the official Jack Webb biography approved by his family.