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: I can be really annoying when I'm on NZT.
Agent Ike: We've noticed.
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.