Goofs

(at around 1h 1 min) The scene involving Sersi is inexplicably flipped horizontally for 3 secs before cutting to another shot, as highlighted by Gemma Chan's upper lip beauty mark now appearing on the right side of her face, along with her hair parting.

(at around 9 mins) Sersi turns the fossil wall hanging into dust to save a little girl. Yet after they get up off the floor, they are clean with no dust in their hair or clothes.

(at around 38 mins) When Thena awakens on the stone altar after first experiencing Mahd Wy'ry, she opens her eyes and parts her lips in the close-up shots, but her mouth is fully closed in the farther shot.

(at around 2h) When Thena follows the deviant into the cave, the camera first shows Angelina Jolie holding a spear and a blade; the scene cuts to another angle where Thena is seen with a spear in one hand and the other hand has no blade visible.

(at around 21 mins) After Gilgamesh punches the Deviant in front of the gates of Babylon, the shadow of the city is close to the Deviant. In the next shot, the shadow is much closer to Gilgamesh. On top of that, Thena appeared out of nowhere on the left of the screen.

(at around 2 mins) One scene shows Earth from space, 7000 years ago. The view shows Northern Africa with the Sahara desert. However, 7000 years ago the Sahara was not a desert but covered in grass, trees, and lakes. The "African humid period" ended 6000-5000 years ago.

(at around 27 mins) In ancient Mesopotamia where the Eternals are helping the locals farm, they are seen to be planting corn (maize), which didn't exist in that part of the world at that time.

(at around 16 mins) The English police car that arrives on the scene after the initial monster attack is playing a continental European siren. The UK has different sirens from the rest of Europe.

The scale of the Celestials is all over the place. When the Celestial emerges from the ocean, it is shown with the head above the clouds, yet based on the size of the hands versus the Eternals, it doesn't make any sense.

Then at the end, the celestial appears large in the sky, and is also shown to be high in space, yet is not really that big in scale against Sersi.

(at around 7 mins) In London, Sersi looks at a billboard advertising the "artifact" exhibition. However, in British English it is spelled "artefact."

(at around 7 mins) When the description "Present Day London" comes up it's looking west with the Shard skyscraper on the south bank of the River Thames. This would mean it's sunset and not sunrise.

It is 'Present Day', aka 2022 AD, as opposed to '5000 BC', when they arrived. It is a reference to time on a historical scale, not referencing a day or night.

(at around 7 mins) Sersi's 9am alarm goes off. When she walks into the Natural History Museum moments later, the clock behind her on the wall reads 8:28. When she then enters the classroom, the clock reads 9:14.

(at around 35 mins) The Tenochtitlan seen in the film seems to be a land-based city, while the historical Tenochtitlan was a relatively small island in a huge lake reached by a system of bridges.

(at around 26 mins) When Makkari is in ancient Mesopotamia using sign language, there are several signs that in those times would have made no sense to the population. For example, the word "time" where she points at her wrist, they would not know what a wristwatch is so that would not have been the sign for time. And because the Eternals are not time travelers, Makkari herself wouldn't have known what a wristwatch is at that time, so her sign language couldn't include that specific sign.

(at around 35 mins) The film's version of Tenochtitlan is shown to have five identical copies of the Templo Mayor, which in real life was a unique structure, equivalent to the cathedral of a European city.

At 21' Lauren Ridloff (Makkari) is conversing with two traders with sign language and taps her wrist for the word "time". It's 5000BC... Not many wristwatches were made back then.

(at around 12 mins) When Dane and Sersi are discussing moving in together, Dane's dialogue does not match what he is saying.

(at around 2h 10 mins) The final confrontation takes place in the Indian Ocean in daylight, but when Icarus looks down at the Earth the sun in shining on it in a way that it should be mostly in twilight or night.

(at around 1h 5 mins) They are speaking Spanish in Druig's colony in the Amazon, but Brazil is a Portuguese speaking country.

(at around 18 mins) Sersi tells Dane that she and Ikaris were together for 5000 years. However the next flashback shows that their relationship started while they were living in Babylon in 575BC and ended a century before the events of the movie, so they were together for 2500 years.

Edit: Technically they have been together for 5000 years just but not romantically together for 5000 years.

(at around 1h 25 mins) Given the Celestials are a synthetic race with regenerative powers who are incapable of aging - present day Phastos shouldn't need to wear glasses.