When Defiance Schneiderman is looking at the phone showing the identity of Jose Martinez the time on the phone is seen as 2:16 PM. When we cut to the next shot with Jane talking to her by the window we can see it is night time.
Nguyen is clearly left-handed as he uses his left hand to start his confession note, yet they show him holding the gun right-handed, as a right-handed person would do, in a previous scene.
When they fly from Austin to New York, there is a short sequence of an airport with the caption "Austin International Airport". The airport is clearly London Heathrow, with numerous British Airways aircraft. British Airways do not fly to Austin.
When Kim is trying to convince Lisbon to help the FBI on their case, she says that Jane stopped the ten-year reign of a mass murderer. Red John was a serial killer, which by definition is a criminal behavior distinctly different from mass murder.