When the woman on the bed at the seedy motel is told the world isn't going to end, she raises her arms to the heavens and says "Thank You". There is no Man In The Sky at this time to thank.
In the bar scene, there is a full glass of beer in front of Mark. When the camera cuts to the bartender then back to Mark, his beer glass is near empty, now accompanied by several empty shot glasses.
When Mark and Anna are in front of the two glass doors after their date, the left door closes twice when Mark is speaking to Anna as she goes inside the building.
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.
During Anna's first date with Mark, the waiter brings her a margarita and mentions he had a sip from it. The glass is about half full. In the next shot with the margarita it is almost completely full.
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.
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.
Although this world has no concept of imagination, religion or gods, Mark refers in his fiction to the planet "Mars," and everyone is already familiar with this name. Mars is named for the Roman god of war who would have never been made up in the movie's world. 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, etc.), when referring to events such as the Black Plague and Napoléon Bonaparte. But since there is no concept of God, and therefore no Jesus Christ, what are the years counting from?
In an alternate world where lying and religion were never invented, the Black Plague and the career of Napoléon Bonaparte happened in exactly the same way as in our history. This is impossible, as both series of unfortunate events were inextricably intertwined with matters involving lying and religion.
Just because you can't lie doesn't mean you have to express what you're thinking all the time, which some people in the movie do.
A number of people wait until Mark is fired before telling him they either hated him or working with him. But seeing as everyone appears to say what they think during every encounter he would have been told this almost every day by the same people. They would not have withheld their opinions until his last day.
Mark seems constantly surprised, even upset, when people are brutally honest with him or about him to others, which should not happen if he has lived his whole life in this society.
Even though Anna can't lie, on her date with Mark she fakes a smile a couple of times.
Mark's boss had difficulty firing him because he had difficulty with confrontation. Firing someone who is incompetent wouldn't be confrontational since it would only involve stating the fact that he is not profitable for the company.