Factual error: The movie is set in 1971, but during the start of the motorcycle race several of the bikes are obviously early 90's Honda CR's and Suzuki RM's. You can tell this from the disc brakes on the front wheels of the bikes and the 90's style plastic fenders and bike colors. Bikes in the 70's generally had metal fenders and definitely no front disc brakes.
Factual error: At the second-to-the-last scene, where Duke sits in the chaos of the hotel room and reflects on the hippie and drug culture he is surrounded by, there are three television screens. One of those screens - the one right in front of him - shows a tank driving from right to left. This tank is recognizable as an M1 Abrams, which entered service not before 1980.