Badge! Gun! - S1-E2
Corrected entry: While under NZT influence he is working ambidextrously on a blackboard drawing a portrait with his right hand and solving an equation with his left. Even my 11-year-old niece (who didn't watch but was told the situation) knew right brain=artistic and creative=left hand, left brain=logical and problem-solving=right hand.
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.
Brian Finch: You remember a lot more than you think you do. Every experience you've ever had, every idea that came to you in the shower and then slipped away while you were brushing your teeth... it's all there for the taking.
Correction: The left brain/right brain idea is a myth, not actually backed up by the science: http://www.livescience.com/39373-left-brain-right-brain-myth.html. Regardless, the whole point of NZT is that it allows you to perfectly use every aspect of your brain simultaneously, so even if the left/right part were true, this shot only serves to demonstrate how effective NZT is at removing those limitations.