Factual error: In chapter 21 Vittoria states that "everything has an opposite. Protons have electrons." Protons and electrons are NOT opposites. The opposite of a proton is an antiproton, the opposite of an electron an antielectron (or positron). Other than having opposite charges, a proton is completely different from an electron, ie. a proton is a hadron made from 3 quarks, Up Up Down, making it a baryon. An electron is a first generation lepton and is a fundamental particle. As a physicist, Vittoria wouldn't make this mistake.
Plot hole: The main reason the antimatter bomb was not found, according to the book, is because it is small enough to be hidden anywhere. However, there was a wireless camera watching the bomb all the time. The wireless camera, just like any wireless device, is basically a radio transmitter and receiver, so all they would need is a device displaying the signal strength coming from the camera (having no such device, the CERN could probably borrow some). Where the signal is the strongest, there is the bomb. It is improbable that there wasn't a single person understanding how wireless devices work.
Factual error: When Vittoria shows Kohler and Langdon the underground lab, she searches for the dial tone on her cellphone (and fails as they are underground), thrice. Cellphones don't have dial tones.
Factual error: In one of his lectures Robert Langdon tells his students that the Christians got their tradition of communion, eating their god, from the Aztecs. The Aztec civilization dates to the 13th century while the tradition of communion is as old as Christianity itself. And even disregarding when the Aztecs lived, the Europeans had no contact with America until the late 15th century and could thus not have gotten any traditions that way.
Factual error: Robert Langdon insists that Harvard astronomer Edwin Hubble proposed the theory of the Big Bang. Hubble never was associated with Harvard.
Continuity mistake: In chapter 21 (page 97 in my British Corgi edition) Vittoria says she and her father collected five thousand nanograms of antimatter. However, in chapter 22 (page 101) when Vittoria is about to remove the trap, Kohler says "Five hundred nanograms!", not five thousand. As there is such a huge amount of power in a tiny amount of antimatter, there would be an enormous difference between 500 and 5000 nanograms and Kohler, as an expert scientist, would know this and not make that mistake.
Factual error: Cardinal Mortati states that he was Devil's Advocate at the late Pope's confirmation. The Devil's Advocate argued against the canonization of saints, not the confirmation of Popes, until the position was abolished.
Factual error: At the end of the book (spoiler alert) the cardinal, Mortati, states that the pope did not sin when he had a child with Maria via artificial insemination. For the Catholic church, this is false. The church condemns unnatural sexual acts between two persons, one of the most unnatural being artificial insemination. The idea that the pope's "devil's advocate" would allow this behavior is absurd.
Factual error: At the fourth altar of science a man is drowned in the Fontana dei Quattro Fiumi, and Langdon swims around in the water. That would be hard to do, considering the depth of the fountain is little more than one foot.
Factual error: According to the book the statue The Ecstasy of St. Teresa was rejected by the pope for being too sexual in nature. Actually the statue was commissioned by the pope for the exact church where you find it in the book.
Factual error: Despite Dan Brown's claim that the facts and places of the book are real and haven't been altered, the geography of Rome is very inaccurate. The map provided in the book is not consistent with a real map of Rome. Interestingly enough, if you try to map out the way to Illuminati's headquarters as it is depicted in the book, neither a real map of Rome nor the fake one in the book will lead you to the same place as it lead Langdon.
Factual error: The book states that Sant' Agnese in Agone is located in the east of Piazza Navona. It is actually in the west.
Factual error: The storyline contains numerous ambigrams as supposed symbols of an ancient conspiratorial order, and even refers to some centuries-old, iron tools that are shaped in the form of ambigrams. However amibgrams were actually invented by Peter Newell (Lewis Carroll's illustrator) in 1893. For such a simple concept it is remarkable that no earlier examples are known, so careful searches have actually been made by art historians. However to date not a single example has turned up from earlier times.
Factual error: The book erroneously claims that St. Peter's Square is not located in Vatican City, but in Rome proper. Although located outside the perimeter wall of the original Vatican complex, it does lie within the boundaries of present-day Vatican City, established in 1929.
Factual error: The book places St. Peter's basilica in the Vatican Museums. St. Peter's is located outside the Museums.
Factual error: Maximilian Kohler makes a point of Copernicus (along with many other scientists) being murdered by the church for revealing scientific proof that contradicted the church. However Copernicus actually died from a stroke. What's more, he was a priest until his death and the Church only suspected him of heresy.
Factual error: C.E.R.N. does not own any aircraft, let alone Thunderbirds-style Mach 15-capable spaceships.
Factual error: Particles only annihilate upon joining their exact anti-particle counterparts, which is to say for example, electrons annihilate with positrons, protons with anti-protons, and so on. Several conservation laws would otherwise be broken. So when the magnetic field within the anti-matter bomb failed, all that could've occurred is the anti-protons would've met with surface electrons in the bomb's inner walls. On top of that, the surface electrons and the anti-protons all have equal negative charges, and thus would repel away from each other, never coming into intimate contact. The bomb would never have detonated.
Factual error: The book claims that St. Peter's is adorned by 140 statues. St. Peter's has only 13 statues - Christ and his apostles.