Factual error: The "big giveaway" that happens at 9pm across the whole country would have to happen at least five different consecutive times due to time zones. The "big giveaway" in the most eastern time zone would be successful, but further west it would be earlier than 9pm.
Factual error: Right after the assassin kills Harry Grimbridge in the hospital, he walks out to his car to set himself on fire. We see him pour gasoline on his face and chest, flick the lighter, and IMMEDIATELY the car blows up. This is near impossible. In order for the car to blow up, fire would have to reach the fuel tank or lines. The body would have to sit burning in the car for at least a little while in order for the fire to properly spread to certain areas where the car could then blow up. Secondly, there have been many real-life instances where bodies have been set afire inside cars and the car has never 'blown up'.
Factual error: At the very end of the movie, we see Dr. Challis rushing to the gas station phone with seconds to spare, calling the "networks" to try and prevent the deadly commercial from airing. Almost impossible for several reasons. First off, Challis only calls one network (we don't know which one) and yet they seem to pull the commercial from two of the three main stations, which is unlikely (not all networks are affiliated). Secondly, without any special credentials, it is near impossible to get something pulled off the air, even in a legitimate emergency. Third and lastly, it seems even more impossible that given all of the above, any of this could have been done in under a minute's time.
Factual error: The story takes time the last week of October. When Challis and Ellie are on their way to Santa Mira, the trees have green leaves. Even in California, this isn't usual.
Factual error: During the scene where Cochran had Dr. Challis tied up in the chair with the mask on in front of the television, Dr. Challis eventually moves the chair close enough to the television, where he literally kicks right through it. This seems highly inaccurate on several levels. First off, Dr. Challis' upper legs were still tied down which would have limited his strength considerably. Second but most importantly, the television itself nor the cart it was on weren't "anchored down" or "bolted down" in any fashion bolstering any leverage for him to be able to put his feet straight through the television. In reality, his feet should have just pushed the tv off the cart and onto the floor.
Factual error: Towards the end of the movie, we see Dr. Challis hide amongst some boxes when running from Cochran's men. Challis then finds a phone on the wall and dials his ex-wife, attempting to warn her of Cochran's plans. When he dials her, he only pushes 5 buttons on the phone. Even without an area code in the United States, all phone numbers have always had 7 numbers.