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 is pretending to be Walter at the end of the movie, there is no visible wound under his chin from the nail that Daniels stabbed him with earlier.
When the Xenomorph climbs down the hole on the ship, its dorsal tubes phase through the floor.
Daniels stabs David in the chin with a nail during their fight. However, though we see David (maskerading as Walter) in need of suture points for his facial injuries, no puncture wound is visible on his chin in the final scenes.
The blood on Ferris's face changes from scene to scene.
The "gestation period" for the Xenomorphs changes from character to character. It takes anywhere from roughly 1 hour with the first "chest burster" to appear to mere minutes for subsequent others to gestate. There seems to be no "standard" length of time before they appear.
Additionally, this contradicts all of the other films in the Alien franchise which this films "precedes" as it as long as a calendar day for Kane's alien implant to gestate.
David explained to Capt. Oram he bred them into hybrids, thus making them grow at different, and faster, rates.
When David confirms one of Daniels orders when they are trapping the xenomorph, his mouth doesn't move at all.
The Covenant crew locate the Elizabeth and Davids crashed alien ship on the mountain, however in a flashback sequence the ship is shown hovering above the alien city with David in complete control releasing the bio weapon.
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.
When Walter and David are quoting from the poem Ozymandias it is incorrectly identified as being written by Byron. It is in fact by Shelley.