Ed orders the Orville away from the binary stars and to Outpost 30. An exterior shot shows the ship flying away from the stars and getting underway. However, after Isaac's grand gesture towards Claire, the camera pulls out of the bridge and the ship is seen completely stationary.
When the ship is visiting the binary stars, it shows them as being so close that their chromospheres are literally touching. This is not possible because the mutual gravity would have long ago torn them apart. In reality, binary star systems are much more disperse. For example, in a "tight" system like Alpha Centauri the stars are 18 AU apart (an AU is the average distance of Earth from the Sun). Some wide binaries, on the other hand, have separations greater than 1000 AU.
While on the bridge scanning the binary star system, Isaac refers to John as "sir." John is not his commanding officer. Isaac could be using the polite form of "sir" as we do today, regardless of any hierarchy.
Isaac says "Reset table" while in the holodeck, but fails to say "Computer, reset table", so how would the computer know he's talking to it? Update: Much the way computers in all variations of Star Trek are tracking everything, The Orville's computer logged what happened and, logically and correctly, knew that Isaac was telling it to reset the table.
Lt. Cmdr. John LaMarr pronounces Porsche as Porsh instead of Porshuh. It is common to refer to a Porche as a Porsh in the US.
When Isaac creates a holographic simulation to make himself appear human, he somehow loses mass. Even if the simulator could somehow make him appear slimmer, when Claire touches him, her hands would come into contact with his original dimensions.
When Ty presses the keys on the piano he is playing, the hammers that would vibrate the strings to produce the notes don't move.
Isaac says that Claire is from Baltimore, which is located in the "north-western hemisphere" of Earth. A hemisphere is a half of a globe. The Earth is divided into northern and southern hemispheres across the equator and eastern and western hemispheres along the prime meridian, but by definition there is no such thing as a "north western hemisphere." There is no generally accepted geographical term for a quarter of a planet, though the term "quadrant" would likely be the most popular term in use for such an area.
Isaac was left on an alien world with human-like inhabitants for 700 years in Mad Idolatry (2017). It is unreasonable to assume he learned nothing of romance in that time, yet he acts completely naive on the subject here.
Isaac sends Claire a message asking her to meet him in the simulator "tonight at 8." The Union uses military time, so it should have asked her to meet him at 20:00.
Kelly says that she and Ed gained a combined 40 pounds during their marriage, remarking, "God we were fat." Flashbacks of married Kelly are seen throughout the series, and no such weight gain is present.
Dr. Finn tells Isaac that, "if a relationship has any chance of working,
it has to matter to both people, more than anything else in their lives." This is incorrect. Even when 2 people are in a committed and functional relationship, other things should matter more. The well-being of their children, for instance. As a medical professional with training as a psychologist, Claire would know this.