As Frank Serpico is driving across the bridge in his Studebaker Lark to report for his first posting as a patrolman in 1960, many of the cars in the background are models from the mid-1960's to early 1970's. (This is true in many of the early street scenes as well.)
In the opening sequence of the movie that shows Serpico having been shot, it is raining heavily while he is being rushed to the hospital in the police cruiser. Towards the end of the movie where this sequence of events picks up again, it is not raining.
Serpico was shot in his face and operated on. He subsequently wakes up after the operation with his beard intact. The hospital would have shaved it to cure the injuries caused by a bullet trespassing his cheek.
In the opening scenes with the patrol car carrying Serpico to the hospital, the unit's emergency light has 3 red bulbs and one amber bulb as it spins. As the unit arrives at the hospital and as they remove him from the back seat the light has 4 red bulbs.
During the shooting gallery scene, Frank and a few other cops are practicing their marksmanship. All the bays are full except for bay two, which has the shooters table up, to allow access to the gallery itself. In the reverse scene, the table is down.
As the cops are monitoring the drug dealer's apartment near the end of the movie, there is a French Renault Dauphine parked in the front of the building. The Dauphine disappears after Frank enters the building. The gray car parked across the sidewalk on the other side of the street disappears as well, once the police bust the 2 users leaving the building.
Prisoners "chain gang" being led into the Paddy Wagon at beginning, had both male and female prisoners on the same "chain," and transporting both sexes in the same wagon. This was absolutely forbidden by the NYPD, then, and now.
At beginning, at the hospital after Serpico had been shot, NYPD Lieutenant (Judd Hirsch) salutes Chief Sidney Green when Green is dressed in business attire. NYPD members only salute superior officers in uniform.
At the apartment raid, Serpico is shown armed with an automatic sidearm, possibly a 9mm. However Frank Serpico has stated that this is incorrect and that he was carrying his trusty Smith & Wesson snub-nose .38 special as he always was (and the other officers were; this is a favorite of plainclothes and undercover officers as it is more easily concealed and drawn.)