Magic Show - S5-E6
Continuity mistake: While Penn Jillette is performing the guillotine trick, in the reflection of the blade, a man is can be seen standing between Charlie and Nikki. He is not part of the scene, and is not visible in any regular shot.
Soft Target - S2-E6
Character mistake: On the roof, Don and the other agents have their weapons drawn on James Grace, who is holding Houseman hostage with the fake bomb. Once Grace is taken away, the threat is gone. But Don still has his gun pointed at Houseman, with his finger on the trigger. Houseman, while Don might think is a jerk, was innocent of any crime. There's no reason an agent like Don would have his gun pointed at him.
Visible crew/equipment: When Don and David chase down Jose Salazar and get him down on the ground to cuff him, a crewmember (presumably the second cameraman shooting Jose's low angle closeups) is lying on his back behind David.
Visible crew/equipment: After the Secret Service agent calls the counterfeiters "our guys," when it cuts to them back at the office at least three actors' T-marks are visible on the floor.
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.
Visible crew/equipment: When Don talks to David about his priorities and the importance of finding Rachel Abbott's car, right after David tells him that the car is not turning up, we can see the reflection of the moving boom pole and mic on the glass door.
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.
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.
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.
All's Fair - S2-E18
Revealing mistake: In the scene where Don and the FBI crew is investigating the body of the Iranian victim, a split second closeup on the head of the Iranian woman shows she is breathing even though she's been dead for an hour already. (00:04:00)
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.
Revealing mistake: When Crystal sets fire to the meth lab, she flings her lighter in a straight direction towards the front door. But you can see that the fire does not start there: it starts in the middle of the front porch, more than three feet from where her lighter landed.
Continuity mistake: When the two police officers visit the dirty lawyer's place, they find him dead on his bed. In the first shot, there's a pillow next to his left shoulder. In another shot, the pillow is right next to his head.
Other mistake: The MP5 carried by one of the Federal officers breaching the meth lab has the magazine facing backwards.
Dirty Bomb - S1-E10
Continuity mistake: When Charlie is writing the result of the calculation for the first time he writes "25,600", but when the shot changes he finishes writing "25600", without a comma.
Continuity mistake: When Jose Salazar is eventually arrested, he is knocked to the ground, and handcuffed behind his back. However, the next shot shows Jose pushing himself up with his own hands. His hands are then behind his back in the following shot.
Continuity mistake: When Bell is in the car with the female assassin, she pulls out a gun and points it at him. The camera then goes to an outside shot, where you can see the car's side window is already splattered with blood, before we hear the shot and the window shatters.
Continuity mistake: When Amita talks to Charlie that she isn't quitting the running of curriculum and he's writing something on the board- he is holding a laptop entering something in it, than camera shows Amita and when it comes back to Charlie- there is nothing on the laptop screen (only black screen). (00:37:10)