When Greg and Mark are being pulled over by the motorcycle cop, the rearward shot clearly shows that they are on a 4 lane street with buildings on each side, and he stops in the left lane near the center line. But in the remainder of the scene they are stopped in the right lane of a long bridge.
Also, the lights on the police motorcycle are still flashing as the officer walks up to confront the driver of the car. Later in the scene, the lights on the motorcycle are not on anymore.
When Mark exits his car when the mob is formed around his house; his seat belt automatically moves up the side of the car, but in the next shot he exits the car without trouble and his seat belt is in the original down position as it would be when he is driving.
John Hodgman, as the "Wedding Overseer" looks to be wearing a crucifix. However, upon close examination, it is actually a likeness of Mark holding the "two pizza boxes", matching the image behind the "Wedding Overseer".
Although lying does not exist, it is obvious that crime does, given Mark's father's depicted history as being a burglar. The policeman is able to commit and continue committing the act of taking a bribe, so long as he is not questioned about whether or not he is doing so by a superior or a fellow officer, as then and only then he would be in a position where he would have to tell the truth.
When the policeman pulls Greg out of the car, you can see that the car is equipped with automatic seat belts, and at no point can you see that the lap belt is buckled. Therefore Greg could be easily pulled out of the car as the shoulder belt retracts, which is shown when the door opens.
Although this world has no concept of imagination, religion or gods, Mark refers to the planet "Mars." This name comes from the Roman god of war who would have never been made up. The planet would have been called something unimaginative like "Red Planet" or "4th Planet."
The world depicted in the movie uses the same dating system as we do (1300s, 1812, etcetera), and remembers the same historical events such as the Black Plague and Napoléon Bonaparte. These two things don't wash. First, since there is no concept of God, and therefore no Jesus Christ, what are the years counting from? Second, the histories of the Black Plague and Napoleon were replete with lying and religion (which were instrumental in Napoleon's rise to power), and without those things these events could not have happened in a remotely similar way.
When Mark is trying to withdraw his money from the bank and system is on again, the bank teller says she can now access his account, but you can clearly see on her screen that she has already been looking at it.