When David is pretending to be Walter at the end of the film, there is clearly no wound under his chin that was caused by Daniels when she stabbed him with a nail. David does not heal the same way that Walter does and the wound would have been recent enough to be visible.
When Karine takes her first water sample, she syringes the water into a plastic container and then closes the lid. This sample is then handed to the marine who closes the lid again.
When David regurgitates the alien embryos and places them in the refrigerator with the human embryos, they are in exactly the same type of capsule and fit perfectly in the compartments. This is unlikely, given that David has been marooned for ten years and thus had no access to current technological advances.
The landing crew are shown walking down the ramp and wading through water upon landing; when running back to the ship the land is dry and they walk onto the boarding ramp on dry ground, when the camera angle changes we see water around the ramp again.
At first glance it appears that when the Xenomorph climbs down the hole on the ship, its dorsal tubes phase through the floor. However they can be seen to be quite flexible, folding back against the creatures body.
When Daniels and Tennessee open the terraforming bay doors at the end, the ejected trucks fall planetward as if the Covenant were hovering rather than orbiting. Earlier, however, shortly before Tennessee descends in the cargo lift (~1:16:45), a full screen monitor displays "COVENANT ORBIT", hence the ejected trucks would stay in orbit until they lost significant velocity, and not fall as depicted.
David claims to have created a "perfect" organism, while in fact the organism he "carefully selected" is inferior to the basic airborne viral organism that attacked the crew when they landed. New "perfect" organism requires eggs/embryo, "gestation period" prior to which a clearly visible "face-hugger" is attached to the host and etc.
At around 24 mins, the Covenant's computer is saying the location of a signal's origin in astronomical terms. It incorrectly says "declension"; the correct word is "declination".
During the opening act, the Covenant is damaged by a "neutrino storm." However, neutrinos are nearly massless particles which so rarely interact with other material that they commonly pass though the entire Earth without ever causing a reaction. They could not damage the ship as portrayed in the film.
In the shots of the first Neomorph emerging, Ledward's uniform can be seen covering parts of his lower back and arms, but immediately after the alien exits and Ledward slumps backward, his uniform is not covering him at all.
Synthetics (Robots) do not grow hair, as David did mid-way through the film. They do not age. They stay the same throughout their immortal life cycle.
The blood on Ferris' face changes from scene to scene.
Near the end of the film, David asks the computer ("Mother") to play the entrance to ValHalla from Act 2 of Richard Wagner's "Das Rheingold". The opera consists of 4 scenes in a single act, and the music is from Scene 4.
When Walter and David are quoting from the poem Ozymandias it is incorrectly identified as being written by Lord Byron. It is in fact by Byron's friend Percy Bysshe Shelley. However, Walter later corrects David on his mistake, revealing that the "perfect" David is in fact deranged.
When Walter removes a damaged embryo from A-3371 there is a small pool of red liquid remaining in its holder which then completely disappears seconds later when he closes the drawer.
Free climbing is with ropes as back up. Solo climbing is what they should be referring to.
Mother gives distances in metric kilometers, but reports the planet's air pressure in psi (pounds per square inch) instead of kPa. A program like this would not mix and match.
In Prometheus, it is established that synthetics like David do not breathe, yet after he fights Walter but before he runs to the cargo lift rescue, he stands at the top of the ramp to look back, clearly out of breath. He also tames a creature by breathing on it and plays the flute.