When Bortus, Klyden, and Topa are having dinner in their quarters, the view of Moclas out of the windows would not be possible given the position of the Orville relative to the planet shown in establishing shot.
When Locar is confessing his feelings to Talla in her quarters, the view of Moclas out the windows would not be possible given the Orville's position relative to the planet in the establishing shot.
The deflector test is declared a "big success" after the starboard array automatically resets, even though for several minutes it did not appear as though it would. In a real combat situation, the Orville's opponents would have had plenty of time to continue firing before the array reset and could have done great damage to the ship, possibly even destroying it. That hardly seems like a successful system.
Bortus explains to Ed and Kelly that Locar was his "kodashik," which he then translates as "an old boyfriend." It has been established that Union officers wear translation devices to understand and communicate in the languages of other species. They should not have needed Bortus to manually translate the term.
While arguing about their jobs, Cassius refers to Kelly as "the commander of a starship." While she holds the rank of commander, the commander of a ship is the person who is in overall charge of the ship, ie the captain. Ed is the commander of the Orville, not Kelly.
While searching the ship for Locar, many of the security officers check in places that no one (save for maybe Yaphit) could fit into, like inside equipment panels or narrow service chutes.
While going over the strange events that have happened to the crew of the Orville with Gordon and Talla, John says, "One time I almost died 'cause I humped a statue," a reference to Majority Rule (2017). John was at risk of being subjected to a "correction" which would effectively leave him with brain damage, but would not kill him.
Two American sailors are seen on the street at the same time. One is wearing dress blues and the other is wearing dress whites. There is no reason they would be wearing different uniforms. Depending on the time of the year they would both be wearing blues or whites, not one of each.