When Michael Burnham and Paul Stamets are dancing in the hallway in the background a lady in a bright red dress and a man walking out of the hallway into a room. Two cuts later they again walk into the same room.
(Around 20 minutes) when Stamets says 'we're almost out of time this loop' he is holding a communicator but in the next shot his hand is empty.
Nearly every episode prior to this one established and reinforced the fact that Saru has "threat ganglia" which permit him to sense imminent danger (or, even more explicitly, "the coming of death"). Yet not once during this entire episode does he sense any danger; to the contrary, he is shown being taken completely by surprise over and over again by Harry Mudd's lethal attacks.
It can be seen at the 23:40 mark that Stamets is not wearing his correct Delta Sheild. He can be clearly seen wearing the mark of a medical officer when in fact he is in the science division. Clearly the costume designers couldn't find the correct badge in time before filming this particular scene.
The Discovery crew's plan to get out of the time loop by rerouting Mudd's communication to Stella and her father, rather than the Klingon ship as expected, only works if Stella and her father were also in a starship within a 30-second warp jump of Discovery's location. The odds of that being the case are infinitesimally small.
Before the time loops start, Burnham and Tyler arrive and the bridge before Lorca calls for the yellow alert. On the next loop seen, they arrive on the bridge after the yellow alert has already been called. If anything, they should have arrived even earlier, as their conversation with Stamets in the corridor, which delayed their arrival on the bridge in both sequences of events, was much shorter this time.
On the loop that begins around 26 minutes in, Burnham approaches Tyler before he has a chance to approach her, as he did in all previous loops. The song "We Trying to Stay Alive" by Wyclef Jean stops playing and Al Green's "Love & Happiness" begins. In all previous loops, "We Trying to Stay Alive" played for several more minutes past when Tyler and Burnham's conversation took place. If the timing of their conversation was moved up, it should have ended later in their time together, not sooner.