The judge's "gavel" is said to be solid titanium. As it is a roughly 6 inch cube, if it were made of solid titanium, it would weigh about 35 lbs. Yet all characters who handle it lift it with ease, including Commander Grayson, a human of average strength who is shown lifting it with one hand.
Reshaping a metal cube into a sphere (by any means - Kitan uses her bare hands) will cause it to heat up to the point that Grayson shouldn't be able to handle the sphere with her bare hands.
While watching Rudolph the Red-Nosed Reindeer (1964), the film skips from Santa asking Rudolph to guide his sleigh the the sleigh about to take off, eliminating the "Holly Jolly Christmas" musical number as well as a scene of Mrs. Claus dressing Santa and approving of his weight gain.
Moclan biology makes no sense. If all Moclans are "males", procreation would be unisexual, and the concept of "male" and "female" would not even be in the lexicon of the race. Also, in that case, all Moclans would be exactly the same genetically (barring any mutations), and look exactly the same (for the most part). Now it is revealed that there are still two genders in the Moclan race, but females are all altered to be males. In this case, the question of how reproduction occurs is still confusing, as it appears that "males" have all the necessary equipment to reproduce and continue the existence of the race (males mate with males), which actually implies the race is hermaphroditic. If that were the case, Moclans which were exclusively female (or male, for that matter) would have been bred out as useless long before the race had developed the ability (and thus the need) to convert females to males.
The Orville's entire senior staff travels to Bortus' tribunal, at least through the ship's fourth officer (the highest ranking known officer on the ship). This would never happen on a military or exploratory vessel, as it puts the ship at a disadvantage should a crisis arise and risks wiping out the entire command structure of the ship if anything happens at the tribunal.
Bortus petitions Captain Mercer to order Dr. Finn to perform the "corrective procedure" on his newborn. As chief medical officer, Dr. Finn has absolute authority over all medical matters, outranking even the captain of the ship. Ed couldn't order her to perform a surgical procedure even if he wanted to.
In the hologram, the leader on the roof cocks the hammer of his rifle, but moments later he operates the lever action, which would actually load the weapon.
Dr. Finn tells the crew that Bortus and Klyden's newborn is 15 lbs 2 oz. Like most science fiction shows set in the far future, the world of The Orville uses the metric system, not the imperial system of measurement.
Claire tells Bortus she "will not perform a sex change on a newborn infant." The term "newborn infant" is redundant, as a newborn is by definition an infant.
When Yaphit is in sickbay complaining of fluid loss and a cough, Dr. Finn tells him that he doesn't have lungs so he can't have a cough. Not all coughs originate from lung issues. As a doctor, Clair would know this.