Factual error: When Mark types email addresses in to tell people about facemash, he writes to several people @harvard.edu. At the time the movie takes place, undergraduate email addresses were all of the form email@example.com. Furthermore, the network brought down by facemash would have been referred to as the FAS network. (FAS stands for Faculty of Arts and Sciences; the eponymous network covered all buildings within the College and Graduate School of Arts and Sciences.).
Factual error: The first three universities to have Facebook in the UK were Oxford, Cambridge and St Andrews. Facebook came to London School of Economics (LSE) in a later roll-out to British universities.
Factual error: In the scene after the opening breakup scene, Mark rushes back to his dorm at Harvard, tapping his wallet against the keyless entry system to his dorm. At the time the movie takes place, all Harvard dorms required the ID card to be swiped.
Factual error: Just prior to one of the early party scenes, someone says that the party is at A E Phi fraternity. Actually, A E Phi is a sorority. The fraternity is A E Pi.
Factual error: The British character Mr. Kenwright claims his daughter is "majoring in French Literature" at Cambridge University in England, but this is an American expression. English universities do not use the major/minor system; instead, students "study" or "read" their subject of specialization (e.g. "she's reading French Literature at Cambridge").
Factual error: The head of Harvard's office is described as one hundred years older than the country dating it as 1676. When the twins leave they break a doorknob and it is given back with the line "here's your 335 year old doorknob" which would place the action in 2011. In fact it's 2004/5.