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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.
Plot hole: The Swiss guard are having great trouble finding the antimatter because it's in a container with no metal components etc., but right next to the antimatter is the security camera. The security camera not only contains metal, but is continually broadcasting a signal they already know the frequency of. Much, much easier to find.
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: 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.
Continuity: 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: 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: 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: 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: 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.