Plot hole: The only reason Kate is brought onto Matt's team is to give the CIA legal authority to operate on US soil. Given that he already has DEA agents and US Marshals on the team, all of whom seem to be fully aware of what he is doing and have no problem with it, this doesn't make a great deal of sense. Her idealism makes her a poor choice for the sort of operations the team is doing, and there are already domestic US agents available.
Factual error: Kate is said to have been on the FBI SWAT team since day one, and therefore has never worked a case from behind a desk. However, FBI SWAT teams are composed of regular field agents who respond to tactical scenarios only as needed, and otherwise carry out normal investigative duties. Unless this is the most overworked SWAT team in history, Kate would certainly have handled at least a few cases from a non-tactical perspective.
Factual error: The lightbars seen on the Mexican Federal Police trucks in Juárez are incorrect - they show both red and blue lights to the front, but actual MFP vehicles show only reds to the front. This is very interesting considering every other detail of the MFP vehicles and uniforms is accurate.