Factual error: It can be argued that the MCU is not quite our world, but certainly mirrors it closely - after all, the movie makes a point to feature real life dates and events such as Hiroshima, showing that even Cap America's actions in Europe didn't alter the outcome of WW2. It's then quite puzzling to see then Sersi gifting the savages in Mesopotamia a golden dagger that reproduces with precision one of the golden daggers in the tombs from Ur; they were Mesopotamian artefacts, sure, but from around 2600 BC and the scene takes place in 5000 BC.
Revealing mistake: During the attack on Druig's village, there's a shot of Gilgamesh and Thena running towards the camera, then stopping as two Deviants fly over them. During this scene, you can see Don Lee (Gilgamesh) briefly look straight at the camera (he's not looking at either the village or the Deviants, since they headed in the opposite direction). (01:13:50)
Continuity mistake: During the interview that establishes that the protagonist is boring, behind Kingo you can see that there's a single seat at the back of the plane to the right of the door on the wall of posters. Kingo is talking to Sprite in front of the posters, and that chair is empty. She blurts out that Kingo abandoned her in Macedonia, and suddenly Kingo gets a reaction shot from Karun that was shooting from that seat. (00:48:30)