Continuity mistake: When Eduardo finds the letter on the mantlepiece about them apparently stealing the idea for Facebook and asks Mark if they did or not, he places a bottle on the mantlepiece just before he finds the letter. This bottle rotates slightly between shots without him touching it after placing it down.
Factual error: The deejay at the 2003 party is mixing with a music software called Serato Scratch Live, which did not get released until May of 2004.
Factual error: Near the start of the film, Mark gets a drink from the fridge and a can of Mountain Dew is visible bearing the newer logo.
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 firstname.lastname@example.org. 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.).
Character mistake: At Henley, Prince Albert of Monaco is introduced as "His Royal Highness Prince Albert." He is a Serene Highness, not Royal. A British VIP would know the difference and say "His Serene Highness" instead.
Factual error: During the beginning of the movie which is set in 2003 Mark is using a Samsung SyncMaster 941BW which was not available during that time.
Continuity mistake: When Mark is filming them on the zip in the pool he is wet. After the doorbell rings you can see his bottom half is no longer wet, when he goes to answer the door.
Continuity mistake: When Sean shows up at the Palo Alto house Mark goes to the refrigerator and tosses Sean a beer. Right after this he tosses a beer to Sharon, Sean's friend. The bottle shatters on the wall and a few pieces get stuck in between the bricks. When the angle changes all of the pieces are instantly gone. A few seconds after this, right after Sean talks to the "wired in guy" the pieces are back.
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.
Continuity mistake: When the twins are rowing we are shown a close up of them talking. After the scene ends the camera switches to a point where we are shown their backs and they are rowing towards us. Their rowing frequency changes between these two scenes.
Revealing mistake: When Mark gets a nasty note from a Harvard classmate and storms out of a computer class, a directory sign saying "USC College of Letters, Arts & Sciences" (ie. University of Southern California, not Harvard) can easily be seen on the hallway wall through the door as he opens it and walks out.
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: 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: 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.