Deliberate mistake: In the scene where they break into the train from its roof, you can notice that despite the high speed and the consistent wind, Captain America's fellows have no difficulties in running, standing up still, and even jumping, like they felt no air resistance. Moreover, you can see that their hair is not moving at all, completely missing to realize any "windy" effect.
Deliberate mistake: The Stan Lee cameo contains a factual error; he's checking out of the Mallrats script and rehearses his lines, but despite coming out later in the year, the movie (and therefore Lee's cameo) had already been filmed, since movie shooting ended in April. Unless we have to assume Stan Lee carried with him all the time scripts of movies he'd been in and randomly read his scenes aloud. (00:30:45)
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.