When Alara and the rest of the away team are running back toward the shuttle in front of the Epsilon Science Station, the two Krill shuttles are missing during the ensuing firefight. When the Orville shuttle takes off, the two Krill shuttles have reappeared in front of the Science Station.
During the discussion on the bridge about whether or not Epsilon 2 has bars or strip clubs the captains chair changes from fabric to leather with heavily padded arm rests.
After the ship takes severe damage to the upper ring the very next scene shows a view from the cargo bay, the upper ring is shown fully intact without damage.
As the crew leave the research building under fire from the Krill, the two Krill ships that landed next to the shuttle appear and disappear randomly between shots.
When the Orville is under attack from the Krill vessel, Gordon says that he can buy them some time if allowed to "wing it." Bortus, who is in command of the ship at the time, tells him to, "Proceed." During the close up of Bortus, the empty captain's chair can be seen off to his right, meaning that he must be sitting in the first officer's chair. In all other shots of the bridge, he is seen sitting in the captain's chair, which would be appropriate for whoever is in command.
During the initial shuttle flight to the Orville, Gordon's reflection in the window isn't mirrored as it should be.
Within a few minutes of each other, Ed and Kelly both use the wrong case for the first person singular pronoun. Ed says "for you and I" and Kelly says "between Ed and I" (both times it should be "me").