Factual error: During his final debate with Professor Radisson, Josh states that science supports the existence of God. There is no scientific evidence to support the existence of any god from any religion. This line is made all the more dubious given that the film earlier made reference to the works and writings of Richard Dawkins and Stephen Hawking - who are two of the most respected scientists on the planet and neither of whom are theists - as counterpoints to his decidedly unscientific claims in earlier debates.
Factual error: Even before his first class is shown, Professor Radisson is given the reputation of being an aggressive anti-theist, with one character even comparing him to the Roman Coliseum. This would imply that he makes students write "God is dead" at the beginning of every semester. This is a form of religious discrimination that would not be tolerated at any public university, especially in a country that is predominantly Christian, and Radisson surely would have been fired for it. It's even said during the concert at the end of the film that Radisson's actions have made the news, but the administration at the university apparently isn't privy to it.
