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.
Suggested correction: The average cop wouldn't be that quick to realise that he could filter the results. Instead of being a plot hole, this is simply a very human initial response to an initial search result.