Character mistake: When Rich refers to the film showing Davis (decades ago), he figures they were in "Asia... Mongolia or somewhere." However, the film cannister had "Tibet, 1937" written on it - important enough to show the audience, but not for the character to read? (00:40:25)
Character mistake: In the epilogue, Charlie illustrates the relationship of mathematics to real life by discussing the golden ratio and its presence in a host of real-life situations, including the shape of a nautilus shell and the distribution of petals in a flower. These claims are disputed by some mathematicians (see http://en.wikipedia.org/wiki/Golden_ratio#Nature), and the one about the nautilus shell one is untrue (see http://en.wikipedia.org/wiki/Golden_spiral#Spirals_in_nature). It's possible Charlie is just repeating what he has read or heard without investigating it for himself, but this is uncharacteristic of him.
Episode #4.1 - S4-E1
Character mistake: Ruth requests a search of London streets with the name "Achilles" in them. A list of streets appears on a computer screen, but when one of them is selected, it is spelled "Achillies."
Character mistake: While testifying during his murder trial, George Vogelman says that he's gone on dates but has never been in a relationship. However, when he sued Ellenor during season 2's "Sex, Lies and Monkeys," he says they discussed his first marriage and his kids, which contradicts his later testimony. While it's certainly possible he could have been lying about having a family, that would mean he was lying to Ellenor about it, but as his lawyer, she takes him at his word as if he didn't have a history of lying.