Plot hole: The motivation of the cult in this film - a dark entity trying to birth their demonic god - is completely different from the cult of the original film, which was portrayed as fanatical Christian witch-burners. No satisfactory explanation is given in the film to explain this and in fact the film explicitly implies they are the same cult on several occasions. The explanation that the cult of the original film is some sort of offshoot or different sect of the cult from this film cannot explain this as it is pure fan speculation and conjecture (thus non-canonical) and in fact raises several more plot-holes.
Plot hole: Ruthven is apparently bitter that he has been denied his chance of becoming an immortal vampire after Clara steals the map from him, which is why he attacks Eleanor. But why doesn't he just go to the island anyway? You don't need to be invited - Clara, Eleanor and Frank aren't. Having been there once, it seems highly unlikely he can't find it again - he's a naval captain, so navigation and observation are major professional skills for him. And it isn't hidden or magically protected - the local boatmen know where it is and are prepared to take people there, although they won't set foot on it themselves. He could quite easily have gone there without the map, entered the shrine and been turned into a vampire if that's what he wanted.
Plot hole: Bobby confronts Wilee on the college campus to give him the envelope. Whilst the confrontation progresses, Wilee gets away from Bobby after distracting him by holding his sandwich by riding his bike off the college campus, onto the main road and never stops. During this ride, he drives past the gaps in several cars and taxis. Within a minute and a half, Bobby then manages to catch up with Wilee. There are two things wrong with the time it took Bobby to reach Wilee. First, there were loads of cars that we would had to have drove past in order to get to him. The problem with this is that Wilee managed to get past the cars using his bike to go through the gaps. Bobby had his car which meant he couldn't have possibly gotten through the gap making him reach Wilee in that amount of time. And second thing wrong with this is, even though Bobby knew where Wilee was taking the envelope too, he still didn't have any way to know the precise direction Wilee was going in to deliver the envelope. (00:11:50 - 00:13:30)
Plot hole: Silva spent years planning his revenge against M, yet the ability to carry out his plan depended on conditions that were entirely out of his control, such as being captured by MI-6 despite having no way of knowing that Bond was coming for him, and only escaping custody because Q triggers the Trojan - there's no way Silva could predict when that would happen, could have been hours, days, weeks, or never. He then ambushes M at the courthouse despite having no way of knowing that she would be there that day.
Plot hole: Marty Mikalski discovers a micro-camera in the cabin and is immediately grabbed by the cursed zombie Judah Bruckner, who drags Marty through the window and plants a machete in Marty's back. In that shot, the machete is obviously buried in Marty's back, which should have broken ribs both back and front, severed spinal nerves, penetrated arteries (as well as the right lung), and protruded from his chest. Marty was dead on arrival in that one stroke. Yet Marty emerges at the end of the film as the hero, with no gushing blood from his back or chest or mouth, and no explanation of how he miraculously removed the machete from his back.
Plot hole: Hock sneaks a gun into the prisoner interrogation area because he is told that guns are not allowed there. If the prison was so strict about keeping guns out of that area then they would surely have metal detectors to prevent such a thing from happening. (00:15:25)
Suggested correction: Not a plot hole at all. Most of the people who are allowed in those areas will be government employees, who will be deemed trusted enough to follow the rules.
Plot hole: When the CIA detects that Matt is accessing sensitive information to track Frost, they trace Matt's location and find out that he is using a public computer in a cafe. We then see that Matt is viewing the same kind of software, files, etc. that the CIA views at their agency. There is simply no plausible way that a random public computer would have CIA software, or be able to access CIA data at all, regardless of Matt's clearance. The computer itself would have to be on a secure domain.
Plot hole: The tracker chips that the program participants have surgically implanted in their legs make no sense: (1) Implanting an RF device in an agent who is going undercover in North Korea, Pakistan, Iran etc. is a very efficient way of blowing his cover. (2) The drone pilots are unable to imagine that the agent may remove or shield the chip, despite knowing that these agents are super-intelligent and resourceful. (3) Why does killing the agent switch off the chip? Even if he's blown apart by a Hellfire missile, the chip should still keep chirping away, safe inside the lump of meat that's left.
Plot hole: They can't find any fingerprints from Nick, but there seem to be quite a few. The door handle and more importantly the window and the sill that he opens to get out.
Plot hole: The killer has been living in the (apparently big enough) crawlspace between walls and floors, for over a decade. There is no explanation (or rationale) given on how he moved the various objects inside every room, closed doors, fed when the house was not occupied, hid the various corpses and, silly detail, concealed his own BO and the stench of his own living quarters, which is something hinted at when they find out his hideout. It is explicitly said that he is agoraphobic and does not get out, ever.
Plot hole: At the end, when billionaire Niles York is mistaken for Frankenstein, how is this possible? anyone who knows him can see it's him, from his appearance (burnt, but not 100%, his face still visible), his voice (doesn't sound like Frankenstein, but does sound like Niles York) & also a simple DNA test would have cleared up his true identity. When he goes back to Terminal Island, people would know it's a different person.
Suggested correction: His plan was always to blow a hole in the tube to have a train crash at that location. This would have caused mayhem and take up a lot of resources (police/ambulance/fire). Bond chasing him had no impact on this part of the plan. Then when his team picked him up, his team would have known where M would have been on that day and would have driven him there. With resources on high at the train crash site, it would have made it easier to reach M.
XIII
This aspect is a bit of a plot hole for me too - one of the factors outside Silva's control is when he can escape MI6 custody, which depends on when Q triggers the 'Granborough' Trojan, which Q only spots with a bit of help from Bond. That triggering could have been hours, days, weeks or never - pretty fraught with risk to rely on individual(s) making that happen at a plot-convenient moment... otherwise Silva has a bunch of associates hanging around London for a few days permanently on a few minutes alert for a random event.