During the brawl in the Cerritos' bar, an officer instructs others to set their phasers to stun. The dual stun/kill settings on phaser weapons were only used in the original Star Trek series and other spin-offs taking place in the 23rd century. In Star Trek shows that take place in the 24th century, as Lower Decks does, phasers use a numerical power scale.
When Captain Freeman is talking to Ensign Boimler in her ready room, she gets up and looks out her window. Her reflection is correct, showing her uniform reversed with her combadge on her left side and rank insignia on the right. However, Ensign Boimler's reflection isn't reversed. His rank insignia appears the left and his combadge on the right.
When Ensign Boimler is called to the bridge from the holodeck, the arch appears for him to exit without anyone calling for it.
When Capt. Freeman and Ens. Boimler are shown reflected in the captain's ready room window, only Freeman is shown in a reflected manner. Boimler is shown in normal view.
Ransom brings a mutation virus back from the planet. Starfleet transporters are equipped with medical bio-filters that are supposed to filter out such infections.
The Red Alert klaxons deactivate as soon as T'Ana begins administering the cure gas through the ship's vents. No one ordered the Red Alert canceled, nor would it be prudent to do so until verifying that the threat was ended, which at that point it was not.
Cerritos officers mutate into black-goo-spewing zombie-like creatures due to an infection that Commander Ransom brought back form Galor after he was bitten by a local insect just prior to transporting to the ship. Starfleet transporters have a bio-filter to remove any infections and viruses during transport to avoid just this sort of thing.
After delivering supplies to the farmers, Boimler and Mariner return to their landing site and casually beam up to the Cerritos with their fellow crewmen. They materialize inside a larger room (possibly a cargo hold), rather than the transporter room, and in the middle of a firefight between the few uninfected officers and the zombie-like crew. No mention is made of who is beaming them up (IE an on-duty transporter chief, who'd either have been infected already or who'd rallied with the remaining crew on deck 8 per the captain's orders), nor why they'd beam (unawares) personnel into the middle of a biohazard and firefight.
When Ransom mutates in the bar and begins attacking people, an officer informs Rutherford and Barnes that similar outbreaks were happening all over the ship due to a virus. Ransom was shown to have contracted the virus from a bug bite and was patient zero for the infection. Unless he went around biting people before mutating, there's no reason outbreaks should have already been occurring, and even then, no reason they'd have occurred prior or simultaneous to Ransom's.
Ensign Barnes mispronounces the word "symbiont."