When the Cerritos finds the Rubidoux the ship is dark, as in a total power loss. On the Cerritos viewscreen the Rubidoux appears dark except when in the next viewscreen shot showing the ships name and registry, lights can be seen in the windows even as the Cerritos bridge crew discuss the dead ship.
When Boimler is rejected from the spa on Endicronimas V, he is thrown into an empty shuttle. But in the next shot, he runs up to the front portals of the shuttle, and Tendi is in the driver's seat.
When phased Boimler is carrying his non-phased duffle bag onto the transport ship, the front of the shoulder strap can be seen through his phased hand, however, the back of the shoulder strap, which should be visible through his phased body, cannot be seen.
When the Rubidoux's survivors are clearing out of the cargo bay, two officers, one a brown-haired human in a blue uniform and the other a blue-skinned alien in a gold uniform, run out with the exact same movement at the exact same time. The animation has been recycled, just recolored and with the hair tweaked.
Mariner contacts Rutherford to use his high-efficiency transporter technology to beam the away team and Rubidoux survivors off the Rubidoux more quickly. Rutherford's transporter technology only beams about half a second faster than the transporter normally operates. Any advantage it gained them would be more than lost by how long it took Rutherword to run to the transporter room and rewire the transporter.
Ramsey's command crew deride Mariner for her lack of professionalism, yet they are openly hostile towards her in the course of their duties. As she has been named first officer in Ransom's absence, she has positional authority over them and such behavior from the rest of the command crew is highly unprofessional as well.
When the airlock is opened and Boimler expects to be ejected into space (before finding that the ship has already landed), he holds his breath. That is the exact opposite of what a person should do in a vacuum. It is possible to survive in space for very brief periods, but if you attempt to hold your breath the difference in pressure will rupture your lungs. Instead, someone in that situation should keep their airways open and allow the lungs to be evacuated, which will be painful but minimize risk of damage. Starfleet Academy covers information like this.
Captain Ramsey asks Mariner, who is acting first officer, to initiate a long range scan. Scanning is usually done by the ops or tactical officers aboard a starship, not the first officer.
Ransom offers to buy Captain Ramsey a drink. The Federation does not use money.