In the shuttle bay, Gordon draws a pistol from his waist and shoots Talla. No pistol was previously seen holstered and it is too large to be concealed under his uniform. As he boards the shuttle, he makes a movement as though he is holstering the weapon, but after that it is once again completely missing.
The ribbon that Captain Mercer puts around Yaphit changes length between when Mercer is holding it and when it is placed around Yaphit's "neck."
When the Krill shuttle requests emergency sanctuary aboard the Orville, Captain Mercer orders Bortus to open the shuttle bay and raise the deflectors. Raising the deflectors would prevent the shuttle from approaching the ship. Obviously the deflectors would only have been raised once the shuttle was aboard, hence the order of the instructions.
The exterior shots show lens flares with dust on the lens. These would have to be programmed in to the CGI. The "omnipresent" exterior camera should not have this effect.
When Orrin is looking through the engineering parts storage section, one of the panels he opens is full of regular 21st century water bottles.
At 19:43, there is a hand visibly resting on the desk in the lower right corner of the screen. It appears that the hand quickly rotates out of view as the camera angle transitions.
When the Krill shuttle crashes into the Orville's shuttle bay, it is met by a team consisting of Commander Grayson, Dr. Finn, Lt. Malloy, and Lt. Keyali. Keyali is head of security, Grayson is first officer, and Finn is chief medical officer. All 3 are appropriate crew members to send into an unknown and potentially dangerous situation where there may be casualties. Malloy is the ship's helmsman. Not only is there no reason for him to have gone there, but he would be needed on the bridge during a tactical situation like the one the Orville found itself in ta that moment. He was only included in the group so that he would recognize his old friend who'd been piloting the shuttle.
Gordon explains to Ed that Orrin, the man rescued from the Krill shuttle, was his best friend throughout his childhood and early service in the Union fleet. It was previously established that Ed and Gordon are longtime best friends (Gordon even got his posting aboard the Orville due to his friendship with Ed). It is highly unlikely that Ed never met Orrin before, or at least heard of him.
Orrin is seen wearing a Union uniform shortly after his arrival aboard the Orville. If he'd been MIA (presumed dead) for 20 years, his commission would not simply be reinstated, especially when he is the subject of an extradition request from a foreign government. He would have no right to be wearing that uniform.