After the opening breakup scene, Zuckerberg 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.
During several scenes at Facebook HQ in Palo Alto, an original "The Facebook" banner can be seen on the site on Zuckerberg's laptop. By this point in time, the word "the" had been dropped and the new logo/banner added.
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.)
After the opening breakup scene, Mark rushes back to his dorm at Harvard, reaching into the refrigerator for a beer. The logo on the can of Mountain Dew was not introduced until 2005. The scene takes place in 2003.
In the meeting Eduardo has with the lawyer to discuss the new stock options he is given the following breakdown on stock ownership: Eduardo 34.4%, Dustin Moskowitz 6.81%, Sean Parker 6.47%, Mark 51% and Peter Theil 7%. These total up to 105.68%.
Sean Parker claims to be the "creator of Napster." Actually Shawn Fanning was the creator of Napster and Sean Parker is only sometimes credited as a "co-founder." In fact, sources are inconsistent as to whether he was a co-founder or early employee of Napster, but none list him as the "creator."
When the Winklevi meet with President Summers, the office building is said to be 100 years older than the USA itself, and "335 years old". However, they are in Massachusetts Hall, the oldest surviving building at Harvard. It was built in 1718, only 58 years before the USA was proclaimed. In 2003, the building was only 285 years old.
In the opening scene between Mark Zuckerberg and Erica Albright, Zuckerberg says that Theodore Roosevelt was elected president because he was a part of the Porcelain Club. Roosevelt was not elected for President, he was on the ballot as Vice President because other politicians wanted him out of the position as Governor. He succeeded to the Presidency when William McKinley died in office, and was only elected president in 1904 after serving nearly all of McKinley's second term.
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.
When questioned about the statue of John Harvard, Eduardo explains that it's not really John Harvard, "It's a friend of the sculptor, Daniel Chester." The sculptor's name was actually Daniel Chester French. (The full name is spoken correctly in one of the outtakes.)
Sean Parker is talking to the college girl in her bedroom. As the scene switches back and forth between them, the girl's sweatshirt changes position several times, on the shoulder, then off, and back on again.
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" can easily be seen on the hallway wall through the door as he opens it and walks out.
Towards the beginning when Mark is putting FaceSmash together, Chris states that Shark Week is broadcasting on the Discovery Channel. The scene takes place during the fall semester of 2003; Shark Week broadcasts annually in July-August.
After being dumped in 2003, Zuckerberg returns to his dorm with what appears to be a modern netbook. This computer is actually an 'ultraportable' VAIO PCG-TR3A which was released by Sony in 2003. Costing over $2000 at the time, this was one of the first laptops that sported a built-in webcam.
The LiveJournal logo on Zuckerberg's laptop in the beginning of the film was not the LiveJournal logo that most users would have seen in 2003. The logo seen in the film was part of a site redesign, a test version of which users were given the option to use instead of using the then-standard layout. Zuckerberg could have opted into the beta test.
Eduardo Saverin was complimented by an investor in Facebook when he said he loved talking to business majors. At Harvard University, business is not an available major. Eduardo corrects the investor by stating he majored in economics, which is true.
During the Valentine's Day acapella performance the girl checking her email remarks that she hopes the links she's being sent are more "cats that look like Hitler." The scene takes place in early 2004, while the website didn't launch until 2006. However, she seems to just be referring to general pictures of cats that look like Adolf Hitler, not the formal website.
During the Saverin and Zuckerberg scene in the Stanford house in Palo Alto, the hallway light switch is off when the "hallway light" is on. However, many residences, no matter how short the hall, have light switches at both ends of the hall for the same light; and if one is in the on position, the other has to be in the off position for the light to be on.
Marylin Delpy, the junior associate attorney, states that she is an expert in "voir dire" and claims it is the process of vetting a jury. In trials, the term "voir dire" can refer both to testing the competency of a witness or other evidence, or the process of examining prospective jurors. She was obviously using the term in the latter sense.
When the Winkelvi go up to Zuckerberg for the first time after he walks out of class. You can see that Josh Pence's face is not replaced for that brief moment, after he is nudged by Armie, revealing that two separate people played the part.
When Mark and Eduardo go outside of the fraternity "Caribbean Night" into the cold, visible breaths emerge directly from their lips. In reality, the breath is invisible for 2 - 3 inches, the space required for it to drop to a temperature at which it can condense and become visible.
The goof items below may give away important plot points.
At the end of the movie, it says that Mark Zuckerberg is the youngest billionaire in the world. That honor actually goes to his former roommate Dustin Moskovitz, who is 8 days younger than Mark. Though, Zuckerberg held the distinction until Moskovitz was named "World's Youngest Billionaire" by Forbes magazine in June 2010.
In the last scene of the film, Mark is seen trying to friend Erica Albright on his own site. In real life, Mark Zuckerberg has unfettered access to anyone's account on Facebook, and he cannot be "unfriended". However, he may instead be requesting her friendship out of courtesy to her.