When the Defiant crew is on their way to the Bajoran sector to recreate the accident 50 years later, Julian is seated on the starboard side of the bridge. Julian's station had always been on the port side of the bridge, behind Miles's engineering station.
When Korena first hands Jake's two books to Benjamin, the one beginning with the stylized A is on the left, and the Collected Stories is on the right. In the very next shot, they're reversed.
Jake continually "writes" on his PADD but the text on it doesn't change.
When Ben Sisko is traveling through time, whenever he appears, his uniform is still dirty and singed from the accident that knocked him out of temporal alignment. When he "snaps back" to the time of the original accident, his uniform is clean again. Since he is physically moving through time, his physical state should remain consistent, and his uniform should still be dirty.
In 2389, Commander Nog is seen wearing the "TNG" style of Starfleet uniform, with the division-colored body and black shoulders, that was put into service in 2366. That style of uniform was phased out by 2371 in favor of the "DS9/Voyager" style black jumpsuit with division-colored shoulders, and retired completely by 2373 in favor of the black two-piece uniform with gray shoulders and division-colored undershirt.
When Melanie is asking about the new collection of stories that the elderly Jake has written, Jake says that he was "tinkering with the last story just this morning." As Melanie came in the middle of the night and the two of them have talked until sun up, he couldn't have been working on the stories "just this morning," as morning had just arrived and he clearly hadn't been working on them. Likely he was confused and meant the morning before her arrival.