Deliberate mistake: During the mob scene outside Saito's love nest, the same black Saab is seen getting firebombed twice. It was shot from two different angles, with the two shots played about a minute apart to give the impression of two cars getting bombed. Also, in the first angle it is clear the car has no engine.
Deliberate mistake: The whole Monaco race sequence is totally (but deliberately) ludicrous. First no driver would be allowed without a fireproof mask and rest of required security measures, as Stark does. Second, the real-life security controls are very strict: When an accident occurs a safety car shows up, flags and audio advices signal the racing cars for them to lower their speed and avoid accidents. Nothing to do with the wild, uncontrolled race depicted here.
Deliberate mistake: When Metro Man flies towards the observatory to save Roxanne, we see a typical "the-characters-see-what-the-audience-sees" shot - a Super-Man-esque shot of him with his arms stretched out in front of him with his fists clenched. This shot is then projected onto a monitor that Minion is watching. It would be impossible to achieve this. It's as if there's some sort of camera on top of the observatory filming Metro Man, which there isn't. We see the observatory enough times to see that there isn't, and even if there was, the angle at which it would need to be at would be impossible to achieve. The shot of Metro Man on the monitor is positioned right in front of him, panning backwards. A camera would need to be very long to achieve this kind of shot, but there simply isn't one present.
Deliberate mistake: When Jared is picked up at the airport in the limo, after the scene where the limo is driving down the interstate it cuts to a shot of several tall buildings. In the street at the bottom of the shot, the traffic is moving backwards if you watch the facing of the vehicles. Looks as if the film plates were flipped. (00:06:30)