When Joe is talking to the man at the car dealership about the old Rambler wagon his parents owned, the man tells him that car came with a "6cyl, automatic with three on the tree" A three on the tree is a manual transmission not an automatic
Joe Dirt maintains his parents car was a 1968 Rambler Wagon made by AMC. When he arrives at his parents trailer park he sees his parents old car in the driveway but the car shown is a 1959 Rambler Super Wagon by AMC.
At the end of the movie when Joe is racing Robbie, Charlene says "do you really think that slant 6 can beat this Hemi" Robbies car clearly lists the engine as a 6.6 on the hood scoop. The 6.6 callout on the scoop indicates a V-8 ("T/A 6.6" for a Pontiac 400 or "6.6 Litre" for an Oldsmobile 403).
When Buffalo Bob gives Joe an Auto Trader he hands him the red copy of an Auto Trader, which is cars priced $5000 or less. He then speaks of a car priced at $14,000 which would have not been printed in that version.
In the beginning of the film, you see the 8 track tape in the player and Joe "turns it up". The label reads "Lynyrd Skynyrd Second Helping" and "Steroe 8" (with stereo spelled wrong). In the next scene when he turns the music down at the guard shack, the label is torn up and not legible.
In the beginning we see Joe Dirt pulling into the radio station in the car he picked up before taking Jill out on a date, but we later see that he abandoned that car on his way to Silvertown when Robbie reads him the note.
The Slant-6 is a Chrysler automobile engine, known within Chrysler as the G-engine. It is an inline-6 piston engine designed such that the cylinders are inclined at a 30-degree angle from vertical. GM Trans-Am would not be using a Chrysler engine.
The goof item below may give away important plot points.
When Joe has his The Wizard of Oz ending, Charlene reveals that she is now missing her thumb and middle finger on her left hand. In a shot in which Brandy unties Joe's bandage, Charlene's left thumb can be seen.