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.
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.