When the Orville rendezvous with the Moclan ship that will take Toren and Korick to the Retepsians, the Moclan ship comes up on the Orville's port side. When the Moclan shuttle leaves the Orville for the Moclan ship, and also when the Moclan ship depart, the Moclan ship is on Orville's starboard side.
When the party from Orville have arrived at the Sanctuary planet, there is a close up of one of the female Moclans revealing a distinct difference in shades between the area around her eyes and her prosthetic (mask).
When Klyden finds Bortus in the mess hall he says that he has been searching the ship for him. The ship's internal systems have been shown to be able to track occupants and relay their location upon request. Klyden would not need to search for Bortus, merely to ask the computer his current location.
Gordon tells Talla that firing on the Moclan ship would be "an act of war." But, as he himself then points out, Moclus is a member of the Planetary Union. By definition, one member of the Union shooting another cannot be an act of war unless one of them secedes from the Union. Even if that could be considered an act of war, so would abducting Union officers, as the Moclans were then in the process of doing.
When the Moclan ship snags the shuttle in a tractor beam, Talla orders Isaac to target the Moclans' emitters. Isaac is the science officer. Firing weapons is done by the tactical officer, seated on the other side of the bridge (likely this was done to give focus to Isaac, a credited main character, rather than the nameless extra who took the tactical station when Talla moved to the command chair).
It makes no sense that Bortus should feel the need to lie to Captain Mercer or the rest of the crew about the infant Moclan, as they openly supported him during the trial regarding Topa.
When approaching the nebula that hides the sanctuary planet, Gordon comments that it must be "over a trillion kilometers across." Earth's solar system is only 287.46 billion km. If Gordon were correct in his assertion, the nebula would be more than triple the width of the solar system and it very clearly is not.
When searching the nebula, Gordon notes there is something "just off our starboard bow." He then points to the star system which is thousands of kilometers away and directly in front of the ship, not to its starboard side.