When they are cracking the 20-digit code to get into the kidnappers computer, they use the dates on his tattoos and arrange them from low to high. You see the tattoos and the numbers are said aloud while they are entered. However the last 5 numbers a said aloud are not the numbers on the tattoo. Problem is the last 5 digits are not the fourth tattoo. You see 9-8-13 but he says 1-12-13.
DNA results are not nearly instantaneous as shown.
As is typical with most Hollywood cop shows, a gun cocking sound is heard whenever a gun is seen. The agents are carrying hammerless handguns when they apprehend the couple with the Camaro, yet their guns are heard cocking when they are seen.
A character says they are heading to Baltimore from Washington DC and to pack their bags. Baltimore is only 38 miles or about 60 minutes from Washington DC and is an easy commute.
Mundo definitively identifies the rial as "Saudi currency". It is also the name of the units of currency used in Iran, Oman, Yemen and Qatar, and could be one of those.
Avery, in Baltimore, MD, responds to the kidnappers ultimatum, and somehow she and the team are in Paterson, NJ (roughly 200 miles away) 30 minutes later to be in on the take-down.
James Van Der Beek, as an FBI agent, jumps into the water to save a kidnapped and (most likely) drowning baby from a just-sunken car. When he reaches the baby, he checks its name tag. He's an FBI agent - he would've rescued the baby whether it was the 'right' one or not. (What? If the name was wrong, he would've just left it there?)
A character says they notified state police and highway patrol for a crime that took place in Maryland. Neither Maryland nor any surrounding states have a highway patrol agency.
No one sleeps with their glasses on.
A character says it will be hard to ID someone since his fingerprints have been burned. He failed to take into consideration a number of other identifiers such as facial recognition, DNA, and dental records.