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.
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.
The ship's computer would not have mistaken David for Walter. In fact, since Walter is a newer model and of likely different chemical composition than David, the computer would instantly detected the difference and wouldn't have referred to the android as being "Walter."
The blood on Ferris's face changes from scene to scene.
When Daniels and Tennessee eject the trucks from the cargo bay, they start to fall towards the planet.
The Covenant spent most of the movie very close to the planet's surface, including near the end meaning the planet's gravity would have an effect on the truck. If the Covenant had been orbiting, the trucks would have merely trailed behind it in the same orbit ; but it was effectively hovering over the planet, so they fell out.
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.
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.
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" because it takes 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.
Correction: The above correction actually creates another, larger, plot hole. This film precedes the original film in the franchise, Alien by 14 years. The Xenomorphs found in that film were apparently brought there inside the ship of the so-called "Space Jockey" a character not shown in Alien: Covenant. There would no way that David could have introduced his embryos to that vessel when the first film makes it clear that the ship they found had been there for many years..certainly longer than 14 or so. In short, the Xenomorphs that exist in this film cannot be the ones which exist in later films.
At the end, David regurgitates the alien embryos and places them in the refrigerator with the human embryos, thing is they are in exactly the same matching capsules as the human embryos and are an exact match for the compartments and fit perfectly. This is impossible as he would have no idea about the refrigerated compartments or the layout of the ship.
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. However, Walter later corrects David on his mistake, revealing that he is not as perfect as he thinks he is.
Near the end of the film, David asks the computer ("Mother") to play the entrance to ValHalla from Act 2 of Wagner's "Das Rheingold". The opera consists of 4 scenes in a single act, and the music is from Scene 4.