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.
Factual error: In the last scene the ICE Train is leaving the station eastbound. It is not possible to enter these trains at the central station because all eastbound trains end in Berlin and have only one station left (Berlin Ostbahnhof). Every ICE leaving Berlin is going in the other (westbound) direction.
Plot hole: After January Jones has just told Liam Neeson she doesn't recognise him. Neeson is trying to persuade Herr Strauss and two cops that he really is Dr Martin Harris of Langmore University, and suggests they look for a photo of him online. However, the cop using the computer says that it could take him ages to find a photo of Dr Martin Harris, as "there are more than 40 000 in the USA." This is very true, but as Neeson has already told him not only his name but also his place of work (Langmore university) in reality the cop would have found the photo far more quickly.
Factual error: Jurgen takes the cyanide out of a coffee tin. He mentions he has had it for years since his time in the Stasi. However, in fact potassium reacts with carbon dioxide to form a harmless compound over time: to prevent this it must be sealed in an airtight container, which a coffee tin most certainly is not.
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.