Other mistake: Throughout the movie, the timeframe of Ikaris and Sersi's relationship seems to constantly change; their first kiss is in 575 BC, but Phastus in 2020 asks her how could she stand him for 5000 years. Sprite tells Dane that they broke up 100 years before, but he leaves her because he can't stand to keep secret from her the mission. Which is a problem, since he mentioned that Ajak told him that when they left Babylon, so around 500 BC.
Other mistake: In 5000 BC, Eternals communicate between themselves using contemporary English. That's only expected in a movie, and they speak with natives using their own language, which some of them struggle to learn, nothing strange. Problem is, several Eternals speak English with a very noticeable accent (Scottish, Mexican, Indian) that predates any time when those cultures/nationalities existed. Lauren Ridloff's Makkari being mute speaks with ASL; American sign language, created in the early XIX century.
Other mistake: When Arishem shows his plan to Sersi, the Celestial emerging from Earth is a huge being that completely breaks the planet apart. In the movie finale, the Celestial's hand and head have popped out, but he's much smaller - thankfully, because if he truly had limbs the size of continents, the planet would have exploded before anyone could do anything about it. At that size (again, judging from lack of permanent damage from his half-birth) it's hard to imagine why his birth is supposedly doomsday.
Other mistake: The Eternal's "Domo" is in Iraq. Phastus gives a radar device to Makkari and tells her to go find the Emergence point. We see her sprint away and pass by the Cristo Redentor statue in Rio, and then end up in a spot in the Indian Ocean (she is holding the global map and we see the landmark) that is practically in the Arabian Sea. So the radar brought her literally around the world to get almost to the starting point. Later in the movie Ikaris flies up in space from that spot, and is staring down at South America.
Other mistake: Ajak uses her power to close wounds on other Eternals and when a creature heals itself everyone thinks it is Ajak's power, indicating she is the only one capable of such a feat. However, in the rest of the movie some Eternals pick up significant injuries, but even without 'the healer' are fine.
Other mistake: Makkari looks for the Emergence using Phastos' special radar that he built. She comes back to base telling them she found the Emergence point, but does not say where it is. Despite leaving early, Ikaris is already there waiting for them; he doesn't have any problem finding it himself.