Helmsman Ortegas is shown operating the forward starboard console on the bridge. Helm was previously established as being the forward port console. The station she is shown at was identified as ops.
When discussing how they cured the virus in sickbay, Nurse Chapel's arms are at her sides in the wide shot, and by her sides in the close-up, but when it cuts back to the wide shot, her arms are suddenly folded behind her back.
When Number One carries Hemmer out of the transporter room over her shoulder, he has clearly been replaced with a lightweight, floppy dummy.
The perspective on the Starfleet emblem on the viewscreen in Uhura's bunk does not match the shot, revealing that it was a graphic added in post-production.
Una orders a complete and total ship-wide blackout, yet numerous running lights are seen in both the staff room and corridors. If they intend to completely starve the infected crewmen of illumination and prevent the light virus from traveling on light waves, they're failing at that objective.
Number One is able to access classified data just by saying the word "override" when the computer informs her the data is classified. Starfleet security protocols require password authentication.
Captain Pike is able to speak to the bridge crew on the main viewer. He only has his communicator to speak with, and communicators only transmit sound, not video. Strange New Worlds (2022) showed that they can be used to transmit video if connected to a specialized terminal, but Pike did not have one on the abandoned planet.
La'an is referred to as "Lieutenant La'an Noonien" or "Lieutenant Noonien" rather than "La'an Noonien-Singh".
La'an address Number One as "chief" when she enters the ready room. Number One is a commander and should be addressed as such. "Chief" is non-commissioned rank.
Just over 30 minutes in, as Una is trying to prevent the warp core breach, there's a quick shot of some misspelling on the panel. Says "Containment Field Has BEN Deactivated" (instead of "BEEN Deactivated").
While waiting out the massive storm, Pike and Spock take refuge in a room with a large window. In the event of a deadly storm, it is much safer to take refuge in an internal, windowless room.
M'Benga shouts at Hemmer to leave the medical systems alone, and Hemmer eventually relents. As chief medical officer, M'Benga has absolute authority over any medical situation on the ship. He is even able to give orders to the captain in such a situation. He should have simply ordered Hemmer not to touch his equipment and Hemmer should have obeyed.