When Laura gets together again with Greg and Gordon enters, her shirt is first half outside of her pants and then completely tucked in her pants.
Laura refers to her apartment as "small." An apartment that size in early 21st century New York is well above average size. She also tells Gordon that she works as a retail salesperson, a job that would not support the level of rent she'd be paying on an apartment that size in that area since she quite clearly lives alone. Television continues to wildly misinform when it comes to actual cost/conditions of living.
When LaMarr turns the iPhone off and on again, the phone is fully restarted in a couple of seconds. It takes a minute or two for a smart phone to shut down and restart.
When Gordon tells the computer to save the simulation, it immediately ends the program, removing the holographic bed and causing him to fall to the floor. Saving a simulation shouldn't automatically end it. It has been well established that the specific command, "end simulation," needs to be given.
Laura, a holographic character, from a program that has been put on pause and shut itself off, somehow sends Gordon a text message in the real world when he is on the bridge. When Gordon set up the link with Laura's phone, he obviously instructed the computer to continue processing the program even while the simulator program was dormant.
There is no explanation given as to why a time capsule, buried in New York 400 years previously, ended up on the Orville. There is nothing that the Orville could do with the capsule that could not have been done on Earth by Earth-based scientists. However, it is stated that the contents are being transported to a museum on Delta Pavonis.
When Lt. Cmdr. Bortus orders "500 cigarettes" from the synthesizer, only 464 cigarettes appear in the machine.
In Gordon's first meeting with Laura, she takes a beer from the refrigerator and gives it to Gordon. The beer has no cap and is already open.
The iPhone from 400 years in the past has two bars of cell service and Wi-Fi.
The area code of Laura's phone was 838. That area code wasn't established until 2017. The time capsule was from 2015.
When Yaphit suggests turning the phone off and turning it back on again, LaMarr somehow knows to use the buttons on the side of the phone to do so, even though it's a piece of technology he's never encountered before and only just was able to power up.
There was no reason for Malloy to walk in on Laura and Greg because the program was put on pause, and should not have resumed playing on its own. He should have walked in on her still sleeping in bed.
Professionally speaking, Doctor Sherman would not allow anyone to touch such an invaluable artifact, a smart phone in this case which contains a treasure trove of data and insights into early 21st century life, for an extended period of time, due to concerns of wear and tear and irreversible damage. Ideally, one would make a duplicate of said object for testing purposes.
In the simulator near the end, as Laura and Gordon are singing together, there's a camera shot from above the bar. One of the bartenders looks at the camera.
When Bortus and Klyden are fighting in their quarters, Dr. Finn enters without requesting or waiting for permission.
After Gordon is confronted by the rest of the bridge crew in the mess hall regarding the unreality of his relationship with Laura, he angrily asks for permission to return to his post, which Ed grants. He would only need permission to return to his post if he was supposed to be on duty but had been called away by a superior officer. Neither Ed nor Kelly called him to the mess hall, he surprised them there, and if he was meant to be on duty, he shouldn't have been in the mess hall to begin with.
Laura texts Gordon that she can't wait to see him "manana." This is incorrect Spanish for "tomorrow." The correct spelling would be "mañana." Any smart phone would have the n with a tilde (ñ) programmed into the keyboard, though it sometimes takes more effort to reach than a plain n.
While at Laura's game night, Ed states that it must be "2300 hours." It has been established, particularly in If the Stars Should Appear (2017), that Ed is confused by military time.