Root Cause - S1-E13
Factual error: Finch's trojan tracker displays "accessing network on IP 623.173.93 .225.9." Not only is 623 an impossible number for an IP address to have, as they only go up to 255, it's also made up of 5 parts, instead of the 4 which IP addresses are limited to.
Lady Killer - S3-E3
Factual error: They show a flight reservation for the young boy's trip to London from LaGuardia to Heathrow. LaGuardia is for domestic flights only.
Panopticon - S4-E1
Factual error: John fires a grenade launcher at a street gang hangout bar front window. Aside from the fact that such a round would hardly have been slowed enough to just roll down the bar, the round is shown complete with cartridge case, which would remain behind in the launcher/gun - it doesn't fly with the round.
Factual error: The bounty hunter, Frankie's, car has a Florida license plate on the front of the car. Florida only issues one license plate for vehicles, and it goes on the rear of the vehicle. (00:15:15)
Factual error: Samaritan launches a cruise missile at the rooftop of 1133 Avenue of the Americas, where a satellite dish is located. A real US Navy Raytheon SM-6 missile, fired from a surface ship, would shoot down the cruise missile shortly after it was launched and long before it hit NYC.