(at around 1h 4 mins) When Atilla puts the broom in the door handle of the guard shack, it is at an ~45 degree angle. The view switches to inside the guard shack and the broom (seen through the window of the door) is now horizontal. Later when the Neanderthal arrives at the shack the broom is again at an angle.
(at around 19 mins) When the receptionist in the archives looks at the old photo, she runs her finger over it. In the next shot, this same hand is now holding the picture.
(at around 26 mins) On the banks of the Thames, Larry and Nick have a talk. The red life buoy box jumps around from left to right behind the actors.
(at around 58 mins) When Lancelot first takes the tablet, the position of the rotating tabs, particularly the center one, changes between shots.
(at around 47 mins) The model of Pompeii is seen being destroyed by lava flow, whereas it was destroyed by ash from the collapsing eruption column.
(at around 1 min) During the opening scenes at the archaeological dig, the British flag is being flown upside down.
(at around 14 mins) The Neanderthal gets incorrectly shocked by an automatic defibrillator. An AED won't discharge if its system doesn't detect a certain type of arrhythmia and the button is pressed.
(at around 1h 4 mins) Nick and Attila lock Tilly in her guard shack using a broom through the handle. However, the door opens outward so it wouldn't have worked.
Many of the exhibits in the British Museum don't exist in the real British Museum.
Sir Lancelot's armor and the castle he calls "Camelot" are from a few centuries after the 5th and 6th centuries when Arthurian legend supposedly took place. However, ever since the 15th century, it has been fashionable in pop culture to "update" the setting of the King Arthur story to a much later time period.
(at around 48 mins) The line "There is nothing to fear but fear itself" spoken by Teddy was spoken by Theodore Roosevelt's cousin Franklin D. Roosevelt in real life. The onset of deterioration causes Teddy to speak many lines that were spoken by other presidents, such as John F. Kennedy's, "Ask not what your country can do for you..."
(at around 55 mins) When Larry mentions he's Jewish, Merenkahre states "I love Jews! We owned 40,000 of them!" This is literally impossible. If Akmenrah is the 4th king, that would make Merenkahre the 3rd king of Egypt. He would have been king around 3100 B.C. However, the 7 year famine that originally caused Jacob and all his family (the Israelites/Hebrews/Jews) to settle in Egypt did not take place until 1708 B.C. Furthermore, the tribe weren't referred to as Jews until the Kingdom of Israel was partitioned into the rump Kingdom of Judah.
As the camera approaches Dexter and Larry from behind, as Larry says goodbye to Dexter, a third hand can be seen by Dexter, presumably, the trainer who is crouching below the table/alter.
(at around 10 mins) In the fund raising banquet scene, the Orion Constellation is depicted with a bow and arrow shooting an apple off the directors head. The Orion Constellation does not have a bow and arrow. He is holding a club above his head. The Sagittarius Constellation has the bow and arrow.
(at around 45 mins) Octavius reads Pompeii upside-down and pronounces it "Iiepwop". As the Romans had neither lowercase nor W, this would indicate he has learned to read modern-day writing (for the purpose of commenting on YouTube cat videos). Consequently he should pronounce it "Iiedwod"; an upside-down P looks like a d. (Although it's never stated, the character could be dyslexic which would explain this last part.)
Consensus among scientists is that the Neanderthal humanoids were intelligent beings capable of elaborate speech, complex and logical reasoning and action, and had sophisticated social and cultural merits. Even for comic relief it can be regarded as backward to portray our common ancestors as brutish idiots, while they should be regarded as extremely skilled survival experts, before climate change, mass extinction of primary resources and brutal invasion and later assimilation and cross-procreation by/with other species of human led to their demise. In short: Neanderthals were not stupid, just less capable of adaptation than Homo Sapiens.
(at around 42 mins) Sir Lancelot makes the comment 'like taking candy from a baby', in the UK the word used is sweets and not candy.