Continuity mistake: In the shoot-out sequence in the Mexican Standoff scene between Archer, Castor, Sasha, Eve, and Castor's two bodyguards, you don't need to look carefully to see that the exact same footage is used twice at different times to show a flowerpot exploding. Also, a bad guy gets shot and falls the exact same way twice at different times. He doesn't even fall at a different camera or body angle.
Continuity mistake: Towards the end of the boat chase, the "Coast Guard" boat is facing towards the two boats. A few seconds later one of the chase boats flies through the Coast Guard boat from its rear. It would have taken too much time to spin that boat around for the boat to crash through the back. And even if it were possible, most of the crew were shot and fell off the boat. Who drove the boat to position it for the crash?
Factual error: In reality, a face transplant like this couldn't work for multiple reasons. Primarily because of blood type, with Castor (Cage) being AB and Sean (Travolta) being O Negative. Organ donors and recipients need to have the same exact blood type for transplants to work, otherwise the recipient's body will reject it even with medication. In addition, intensive surgery is needed to connect a donor face to a recipient (ex. Connect blood vessels), which takes more than several hours.
Other mistake: When Archer (as Troy) and Dubov are fighting with the guards prior to Archer escaping, we see two guards looking at a computer screen which has several prisoners names registered on it, including Pollux Troy's name. Pollux has already been released from the prison by this stage, so his name should have been removed from the prison's computer system. (01:06:50)
Visible crew/equipment: When Pollux falls through the glass roof, you can see his harness pulling him back.