The amount of Mariner's arm that the blue nanobots have eaten changes repeatedly between shots.
When Tendi reverts from a scorpion back to her humanoid shape, parts of her uniform that were shredded in her initial transformation as suddenly intact.
When Rutherford is exposed to the frog bones and his entire body swells up, his cybernetic cranial implants balloon up as well.
When Boimler imagines that he is Captain Riker for inspiration, he pictures himself on the bridge of a Galaxy-class starship, like the Enterprise D. Boimler served with Riker on the Luna-class USS Titan, not the Enterprise. Riker was only an acting captain aboard the Enterprise very briefly. He never commanded the vessel on a full-time basis. The Titan was his first command.
The "Redshirts" introduce themselves to Boimler as a group that help one another rank up. They must not be very good at their stated purpose, as all members of the group are still ensigns, the lowest rank a commissioned officer can hold. Yet Boimler takes their advice anyway.
When Ransom and Kayshon lose track of the Pakled spy, they could have put out a ship-wide alert to have the whole crew help locate him, rather than running around trying to search the entire vessel themselves.
Boimler tells the replicator that he wants a birthday cake with lit candles of varying temperatures. Candles will all burn at the same temperature. (In fairness, this might have been intended as a joke. Boimler isn't exactly Einstein.)