Continuity mistake: When Charlie Epps is writing a quadrillion on the whiteboard, the writing alternates between shots. Most noticably when he first writes it down, there is a significant downward tendency of the 000 groups. In the next shot, they are pretty much horizontal. Also the shapes of the commas alter.
Add timeRonnie Bischof
Continuity mistake: While the mother is driving her children to school in a minivan, both the driver's seat and the front passenger seat change from having the headrest/whiplash protector being attached to the seats (non-removable), to having the adjustable kind that have been removed.
Factual error: In the beginning of the episode, Charlie is stating that "there is always a solution" and "if there's any limitation it's got to be in the mathematician, not the math". Unfortunately, according to Kurt Godel's incompleteness theorems, this is not true. Simply put, there are mathematical problems that cannot be proven/solved.
Factual error: The Secret Service agent says the bills are counterfeit because you can see the watermark under a uv light, which is completely wrong. The uv reactive strip is not a watermark, it's a plastic strip embedded between the two layers of the bill and fluoresces under uv as a security measure. In older bills, it glows blue as in the film. In newer ones, it glows yellow to orange and is on the right half of the bill. A fake bill would be the one that does not glow.
Factual error: Season 1, Episode 10, "Dirty Bomb": The opening figures refer to "500g of Nuclear Material." These are the wrong units to determine the hazard level in a radiological sample. The "Curie content" describes, roughly, how much radiation will be given off, and is not tied directly to the sample's mass. 500g of Cesium-137 (the isotope being discussed in the episode) could well be less radioactive than 1g of a different isotope.
Add timeRooster of Doom
Continuity mistake: When Charlie is comparing a computer wipe to a data scrubber, he first crosses out the equation"E=MC2" with a magic marker, beginning mostly with uniform, vertical lines, and then lightly scribbled. However, in a later shot in the sequence, the cross-out is different, being mostly scribbled, with few vertical lines.
Continuity mistake: When Charlie explains that his map was generated by an equation he writes the equation in abbreviated form on the whiteboard, and also when he writes the equation for the probability of winning the lottery, in following shots the handwriting changes and some of it vanishes and reappears.
Add timeSuper Grover
Visible crew/equipment: After Charlie tells Alan that he and Amita have a lot of work to do and that Alan's hovering over them, when Alan walks away from the table we can see the actor's tape marks on the floor where he had been standing, and also more blocking tape on the rug and kitchen floor.
Add timeSuper Grover
Continuity mistake: While Don's at the parking garage with Rachel Abbott's car he realises that the killer had been watching Karen Silber's house, and when they rush off to her house there are white security bars on the windows and front door in the long shot and also later in the news footage, but when they're at her house none of those bars exist and the shrubbery also differs.
Add timeSuper Grover
Factual error: When Charlie describes the Uncertainty Principle, he is actually describing the Observer Effect, a concept commonly mistaken for the Uncertainty Principle. The Uncertainty Principle actually states that the position and momentum of a particle cannot be accurately known simultaneously.
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.