When Claire is in the parent/teacher conference, her hands go from on the desk in front of her, to in her lap, and back again repeatedly between shots.
After Bortus explains to everyone what the Ja'loja is about, Ed and Kelly go to Ed's office to talk. In the long shot, when she presents him with a hypothetical, a lock of her hair is shown going down the left side of her face. However, it is tucked behind her left ear in the next shot.
Claire asks James if she knows his parents. The Orville only has a crew compliment of 300 people. Furthermore, she is chief medical officer and therefore everyone on the ship would have to report to her for any medical issues or even regular evaluations. It is unlikely that she wouldn't have easily researchable files of everyone onboard. However, the question may be a psychological exercise for James, with Claire playing the role of coy interrogator.
When John freezes the simulator program of the bar, the people sitting at the table behind him are larger than he is. The bar and John were filmed separately and John was superimposed over the bar footage, but the scaling was not correct.
James's parents request that Marcus be placed in another class to keep them separated. The ship is very small, only 300 occupants and only a handful of them civilians and/or children. There would not be enough children of a given age group to have multiple classes of the same grade level.
A third boy is involved with James and Marcus in the food machine hack, but after they're caught, the third kid is never seen or mentioned again.
To prove why they shouldn't be together, Kelly presents Ed with a hypothetical requiring him to sacrifice either herself or Bortus on a mission. She says he would never send the woman he loves to her death, thereby devaluing Bortus' life. The flaw in her reasoning is that Ed has just confessed his love for her, so she is the woman he loves whether they decide to reconcile their marriage or not. The only way to remove Ed's bias towards one of his officers would be for her to leave the Orville, not simply for them to not pursue a romantic entanglement.
Bortus tells Alara that there is a crewman under his command who also lacks a mate. This crewman is later revealed to be Dann. Dann is not Bortus' direct report. Dann works in engineering and is under Lt. LaMarr's command.
Ed only engages the shuttle's cloak after he's been spotted by Kelly. If he'd intended on spotting her in her quarters, he should have had the cloak running before approaching the windows.
Cassius is worried about going public with their relationship because of the effect he thinks it may have on Ed. Cassius says that "the first time you see your ex with another guy can be debilitating." Ed already saw Kelly with Darulio, so her taking Cassius to Bortu's Ja'Loja would not be the first time he'd seen her with another guy.
After Isaac successfully defends Marcus in the parent/teacher conference, Dr. Finn asks him if he will be her date the Bortus' Ja'Loja. Isaac was already invited to the Ja'Loja on his own. He would not need to be brought as Dr. Finn's plus-one.