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 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 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.
Walter's Southern accent comes and goes throughout the movie.
When the energy sails are nearly deployed, we see a computer hologram depicting their progress. This hologram has the sails moving much faster than the actual sails shown in exterior shots of the ship.
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".
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.
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.
When the crews are on the planet, at various points, the beams from their laser sights are sometimes obviously misaligned with the weapon's barrels, notably canted up on occasion.
When the landing craft leaves the mother ship in orbit to land on the planet, it accelerates forwards to descend to the planet. The Mother ship was in orbit so the landing craft should have turned around and gone the other way to slow down in order to descend. Going faster would take it to a higher orbit...
During the opening act, the Covenant is damaged by a shockwave after Mother detects a "neutrino storm". Nutrinos 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. However, the ship wasn't damaged by a neutrino storm at all, but by (as the crew puts it) a "highly charged shockwave from a stellar ignition" (e.g. a supernova) and/or a "spontaneous stellar flare". A neutrino burst is merely something that occurs during a stellar ignition event but is not the cause of the event or any resulting shockwaves from it.
The planet has, what appears to be (cultivated, Earth-like) wheat: yet there is no sign of (animal or insect) life to the exploratory crew - so how is the wheat pollinated? However, wheat does not rely upon insect pollination, and is wind-pollinated (a process called "anemophily"). Additionally, upon discovery of the wheat, the crew mentions that it is very old and so it had likely been there for years.
After David cuts his hair after meeting Walter, the color of his hair changes from blond to brown. David would not have a way to color his hair, or even that quickly, on a primitive planet. However, we can see that David's hair has darker roots (he was seen bleaching it in Prometheus to look like Peter O'Toole) and he was simply cutting away the remnants of blond that he had allowed to grow in the intervening years.
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.
Like in so many other Science Fiction movies, the space suit helmets in Alien Covenant are depicted with inside lights that illuminate the face of the person inside. This would of course be totally impractical, as it would greatly impede the person's ability to see outside. However, this is a deliberate stylistic choice by the filmmakers and not a goof.
In the second half of the movie, in the first scene where Daniels is sitting on the ground out in the rain by the laptop asking the crew on the ship to drop the cargo lift we can hear her voice loud and clear, but her mouth is not moving.
When David abruptly stops playing the piano to ask a question, the last four notes he plays are three identical notes, followed by one higher note. But to play that higher note, his hand moves left, toward the low end of the keyboard.