Factual error: When discussing a recent search of a suspect's home, Hill Harper says "we got his hard drives", but pulls a computer power supply out of a bag. Hard drives are significantly smaller and don't have a bundle of wires coming out the back of them.
This Is Your Brian on Drugs - S1-E11
Factual error: After Agent Rooks has taken NZT he does Sudoku puzzles. When Brian is flipping through the puzzles, the first 2 pages seem OK, but after that, the rest of the puzzles are filled in wrong, not a mistake someone on NZT would do.
Stop Me Before I Hug Again - S1-E13
Character mistake: In Brian's "Laws I Have Broken Since Joining FBI" list, item #30 misspells the word "recorded" - "30) Recoreded NFL Game Without Consent." He'd only have that knowledge if he was using NZT, and if he was, he wouldn't make a mistake like that.
Continuity mistake: Rebecca tells Brian that Chris received the call from his brother to meet and hand the bag off at the park at 4pm. In the next scene, Brian says, "Chris wasn't handing the bag off until 6, so I went straight into training." 2 hour time difference there.
Character mistake: When talking about Mike and Ike giving them descriptions while on NZT, he mentions that he once heard Ike's name but forgot it. Completely impossible since his memory is impeccable on NZT.
Undercover! - S1-E15
Factual error: When in the search for Lucy Church, Brian says he is looking for a blue 1968 Ford Mustang. The mustang in the episode is either a 69 or 70 coupe. (00:05:30)
Fundamentals of Naked Portraiture - S1-E14
Audio problem: When Brian and Rebecca arrive at GERD (Global Enterprise for Research and Development) and Rebecca says, "It's people like this who decided mutually assured destruction as the best way to deter nuclear attacks", her lips don't match her words when she starts speaking.
Revealing mistake: During the "power outage" when Brian is out on the street during the day, all the stop lights and cross walks are on - you can also see the lighting is on in the windows of office buildings.
Other mistake: When Brian is using the right computer and thinking about the murderer of Paul Wilkerman, the computer screen is turned off. (00:31:40)