The swinging doors to the saloon squeak loudly when Saru and Tilly enter but are nearly silent when Zareh and his men enter.
When asking Saru why she was brought on the landing party, Tilly, who Saru identifies as an engineer, asserts that there are many engineers aboard Discovery, including Georgiou. Georgiou is an empress from another dimension turned secret agent and has never shown any engineering aptitude.
When Tilly and Saru are on their walk away from the stranded Discovery on the nameless planet there are three people clearly visible walking around far behind on a hillside. (21m34s) One has a blue jacket, one a white and one a black one. Shortly before (~20m40s) the same three appear as well but only for the fraction of a second and this time staying together.
Saru has been shown to be much faster and stronger than a human being, a fact he does not exploit at all during the confrontation with Zareh when there was ample opportunity to disarm him.
Zareh sends Tilly back to Discovery to get the dilithium with no protest from Saru. Ignoring that a senior officer would volunteer themselves for a dangerous mission over one of their subordinates, Saru can run at 80 kph, more than 10 times faster than a human.
Reno and Saru both decide that they are not on their intended destination planet of Terralysium based on superficial geographic features. Since they are nearly 1000 years into the future, it is not reasonable to make such conclusions based on such thin evidence, as it would be entirely possible that the climate could have changed in the intervening centuries.
Zareh makes reference to Saru's 72 crew members, which Tilly corrects to 88, stating that, "Our wounded are still our crew." Since neither Tilly nor Saru gave Zareh a headcount of their crew, or how many were able-bodied vs. injured, Zareh must have scanned the ship himself, which would have shown 88 life signs aboard, not 72.
Lt. Detmer receives a major head wound (possibly also affecting her cybernetic cranial implant) that is never fully addressed. Her physical symptoms are later passingly attributed to stress.
While walking from the Discovery to the settlement, Tilly asserts that "No one's ever been here before. No one's ever had to describe what this was like." Even if the planet turned out to be one that the Federation had never charted within her original lifetime, to say that no one has ever been there in the intervening 930 years is preposterous. There are inhabited settlements on the planet. People have definitely been there.
While discussing repairs to the communications systems, Saru addresses Georgiou as "commander." Since she assumed the identity of her prime universe counterpart, her rank is captain, not commander. Saru has no authority by which to demote her.
Zareh points a gun at Tilly and threatens Saru that, "You won't live long enough to watch her die," a threat that makes absolutely no sense.
While discussing repairs with Stamets, Reno mispronounces Nilsson's name as "Nielson."