Tilly is shown to be waking up first. Yet the original scene of them in the wormhole shows her waking up after Saru yells at everyone to go back to stations.
During the first time jump, Saru can be seen laying in back of the captains chair. Yet the scene is supposed to have Saru in front of the chair not behind it as that is what is shown in the original scene.
The first time the time bug activated, Burnham and Rayner are at the opposite ends of the ready room table. Yet when the setting shifts to the first instance of time traveling, they are in front of the table.
When Stamets tells Rayner 30 seconds left, he continues to talk way over the 30 seconds told to him.
When Burnham and Rayner fight the Emerald Chain Regulators in the Discovery corridor, Rayner is punching them in the face....while they are wearing helmets with face visors down. Not only is this ridiculous, but what's even sillier is that he seems to be managing to knock them out.
In the flashback to Mutineer Burnham's time line, it is not logical to assume that Future Burnham is actually a changeling as opposed to her actual future self. Why would a changeling take on her appearance but make it so different & difficult for her to believe? A few personal questions could confirm or refute Future Burnham's story.