When Mariner is arguing with Fletcher, the bunk behind her changes numbers, from A12007 to A12003.
When Badgy is following Tendi and Rutherford up the monastery steps, in several shots the two lines shaved into the right side of Rutherford's hair are missing.
When Badgy has Rutherford pinned down in the snow, in the reverse shots his legs are coming out of the sides of the delta emblem shape, but in the forward shots they are coming out of the underside (which is consistent with his previously-established anatomy, such as it is).
After Badgey stabs Rutherford with an icicle, he pulls the icicle out and it is clean, with no blood on it. After Rutherford snaps Badgey's neck, the discarded icicle can be seen in the snow next to them and it is covered in blood.
The Drookmani attack the Cerritos by throwing pieces of a derelict Antares-class freighter at it. The Antares-class freighter, like the majority of Starfleet ship designs, features 2 warp nacelles. The Drookmani throw at least 3 warp nacelles at the Cerritos. They couldn't be the same nacelle(s) thrown repeatedly, as they are seen breaking apart upon impact with the Cerritos' shields. When they throw the main section of the derelict ship's hull at the Cerritos, both of its warp nacelles are seen to still be attached, so there were at least 5 nacelles present when there should have only been 2.
After recently-promoted Lt. Fletcher transfers to the USS Titan, he is still seen wearing the California-class style of uniform (division-color body with a black, white-trimmed shoulder yoke and a chest flap). Personnel on the Titan wear the "First Contact" style uniform (black body, gray shoulder yoke, with division-colored undershirt).
At his promotion ceremony, Fletcher is given a second solid-gold pip, indicating a rank of full lieutenant. He was previously an ensign. The next rank up from ensign would be a lieutenant junior grade (signified by one solid gold pip and one gold-rimmed black pip). He was essentially double-promoted.
While discussing Mariner's confrontation with Dr. T'Ana, Fletcher refers to the doctor as a member of the "bridge crew." While she is a member of the senior staff, being as she is a department head, she is not part of the bridge crew, as that term refers specifically to people who serve on the bridge of the ship. As Chief Medical Officer, T'Ana, naturally, serves in sickbay.