Many of the hair styles are not very accurate or representative of the mid-60s. However, the one that seems most egregious was that sported by actress Pat Hemingway, one of the two car hops. Her hair is in the style of the famous Farrah Fawcett swimsuit poster of 1976.
In the speed shop as the guys are admiring the custom job, Duke [Tony Danza] asks a mechanic if the color is "piss yellow". Instead of using the character's name, the response was "no, it's Tony Nancy yellow". One of the actors is the real Tony Nancy, a well respected muscle car customizing giant. That shade of yellow was his signature color.
When Newbomb is making the tape in the girls bathroom he says "...Tubby's drive in." Yet when it is played at the party the tape has added dialog. It now says, "...Tubby's drive in this Halloween night."
In the speed shop with the customized yellow Ford, Duke leans in from the left side to put in an 8 track tape which meant he had to use his right hand. When the tape player is shown, a left hand is inserting the tape.
When Dudley comes up to the car containing Mrs Friedman and Nevins, he puts his band hat on the top. When he leaves in a hurry, the hat is still on the top. In the next scene he is seen wearing the hat.
At the end of the film when the pledges arrive at Tubby's with their tires, the patrons cheer them on, one customer a short brunette with her hair pulled up in a very very short red dress is standing cheering as they go by, there is an edit to long shot for 2 seconds and then a tight shot on Simpson and a carhop for 3 seconds then a shot showing the same brunette in the red dress is now standing inside a convertible car kissing a guy and pulling him into the car with her.
When Clark and His partner are arguing about the Lawrence of Arabia. You can hear a female voice say what the hell is the difference as officer Bimbeau is saying horse shit this could be a crew member.
At one point in the film, Jimmy says he's going over to Vietnam just for training, but before that, he says they're only sending advisers. In reality, the U.S. had already committed to large scale involvement in Vietnam, due in large part to the Tonkin Bay Incident in August of 1964.
Smitty tells a story about installing a 'Thunderbolt' engine in a Jeep, presumably a 'Willys'. It would be impossible to install this engine into a Jeep. A P-47 'Thunderbolt' has a Pratt & Whitney R-2800 Double Wasp engine. It is an 18 cylinder radial engine that stands 52.8" tall and weights in at an excess of 2300 lbs. A 'Willys' Jeep measures 72" tall (to the canvas top) and weighs as much as the 'Thunderbolt's Wasp' engine.
In 1964 Ford introduced the Fairlane 500 "Thunderbolt". Which was a very limited production drag racing package that included a 427 CID (7.0 L) V8 race engine with two four-barrel carburetors on a high-riser manifold rated at 657hp. I believe that is the engine Smitty is referring to.