Character mistake: When the EMTs are resuscitating Dr. Harris, they use a defibrillator despite their being on a wet metal dock. Not only is this highly dangerous to absolutely everyone present, it would be completely ineffective at restarting his heart as the water and the metal would dissipate the electric current too much for it to do any good. At the very least, they would have stabilized his spine then moved him to a dry surface before beginning defibrillation. (00:08:30 - 00:09:10)
Suggested correction: External defibrillators are self grounded and so can be safely used on wet or metal surfaces. https://danboater.org/travel-health-and-safety/are-aeds-safe-to-use-in-wet-environments.html.
AEDs are indeed safe to use in wet areas - but in the film, it is not an AED that is used. AEDs are automated, and not operated by humans, so as to reduce risk. Your link explicitly states the rescuer must not have direct contact with the body: they just apply the pads, then move back. In the film, it is shown in detail that the medic applies the paddles and then operates them while still in contact with the body. The mistake stands: it's a traditional defibrillator, thus incorrectly used.
Character mistake: The private detective tells Liam Neeson he believes his story, incredible as it is, because as a former Stasi agent, they could spot an innocent man, because an innocent man always stuck to his version of truth while a liar reformulated his ideas. However, in fact the Stasi taught exactly the opposite idea: for them, a liar has invented a pre-programmed version of the facts and cannot change it, while someone innocent can change his speech.