Old Wounds - S1-E1
Character mistake: After Mercer's speech to the entire crew he dismisses everyone except for the senior staff but everyone, including the senior staff, starts walking away as if they were dismissed as well.
Suggested correction: They were walking away, but not as if they were dismissed. The group of senior officers and Mercer are in a completely different part of the room (or possible an entirely different room). Notice the doorway where Mercer is standing. At the beginning, he's in the doorway and it has a white boarder and a 2nd set of doors. Then he's standing in front of a doorway with a blue boarder and no 2nd set of doors.
Such Sweet Sorrow: Part 2 - S2-E14
Character mistake: When Tyler arrives in the Klingon ship, Captain Pike says "calvary arrived just in time." The word is "cavalry." The subtitles show "cavalry."