At one point, Bligh calls Friday and Gannon detectives. They aren't detectives. They are plain clothes officers. If they were detectives, their titles would be Detective Sgt. Friday and Detective Gannon, instead of Sgt. Friday and Officer Gannon.
In the end scene, when the camera pulls back to show the fictitious TV show's cameras filming Friday & Gannon, it reveals that their panel was sitting way too far from the audience for Friday to have casually flung the Make Love Not War pin back to the hippie and for it to reach him. (Friday did not toss it with force vertically, he merely flung it casually to the side.) Yet the hippie wasn't sitting in the audience. He was only sitting on the other side of the host on the panel, close enough for the pin to have easily reached him.
Bill Gannon mentions being 45 years old when he and Joe Friday talk to the makeup man for the TV show, but Harry Morgan was 53 years old in 1968 when this aired.
Sgt. Friday says he's been on the force for twelve years, making it 1956 when he joined the LAPD. However, 'Dragnet' began on the radio in 1949, with Friday on the force for some time (if not twelve years) even then.