Factual error: In several episodes (notably in Season 4 episode 13 - Chuck Vs. The Push Mix), General Beckman, the Director of National Intelligence, refers to "my superiors." First, the DNI reports directly to the President of the United States. Also, a Brigadier General would never be elevated to that position. Thus far, all of the DNIs have been civilians, but if a military officer were appointed (presuming this would be legal) it would certainly be a four-star General, who would likely immediately retire from the military and then be appointed to the position (David Petraeus taking the CIA Director appointment comes to mind).
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Factual error: A recurring mechanism in the series is if the power fails the prison cells that are magnetically locked open immediately. No magnetic locks are designed like this. They would fail their initial purpose which is to provide physical security. If a power outage occurs it would take hours before the locks would be released.
Continuity mistake: In the series finale "Chuck versus the Good-Bye", Chuck and Sarah are in the Wienerlicious waiting for Quin to show up, Sarah begins rearranging the cups. There are three stacks of cups, and after she has set the third stack down, the camera cuts and she is now just reaching for the third stack. (She moved the third stack twice.)