The entire episode of VOY "Relativity". It gets time travel wrong (and yes I know Star Trek makes up rules for time travel), and disregards continuity of previous episodes and movies, in order to tell their story.
That was a (mostly) enjoyable episode for me. I don't know how it gets it "wrong", star trek has never been consistent in how time travel works.
Well Time travel...who does get it right? But what were the continuity problems in that episode?
The entire episode of VOY "Relativity". It gets time travel wrong (and yes I know Star Trek makes up rules for time travel), and disregards continuity of previous episodes and movies, in order to tell their story.
How so?
First
Well the premise and plot of "Relativity" is Temporal Star Fleet is using 7 of 9 as an agent, in order to stop Captain Braxton from destroying Voyager.
However, Captain Braxton himself said that he had no recollection of the events that happened to him during season 3's "Future's End Part 1 and 2". Because that timeline no longer existed and the Braxton who Janeway met and the end of "Future's End Part 2", had no idea who she was. Then in "Relativity", he's trying to get revenge on her for what happened in "Future's End".
Second
Next are the continuity issues brought up in "Relativity".
In "Projections", the Doctor says that he was activated during Caretaker incident. In "Relativity" we see he was activated in dry dock.
Janeway talking to the Admiral about wanting Tom Paris as a pilot for VOY. She says she feels he deserves a second chance. Although in Caretaker, Janeway says she only want Tom because he was a Maqui and could navigate the Badlands for her. Also Tom's "history" with Chakotay was another reason Tom was selected.
Temporal Starfleet and Seven of Nine not understanding pogo/predestination paradoxes. Seven is asked by a Temporal Starfleet guy to give an example of a Pogo Paradox. Seven tells the story of the Borg's attempt to assimilate Earth. Events we saw in the movie FC. However she incorrectly states what we saw, and what the ENT-E crew saw and experienced as part of a causality loop. When it is not.
2373 Earth before Borg time travel
2373 Earth after Borg time travel. Complete with an atmosphere containing high concentrations of methane, carbon monoxide, fluorine and a population of nine billion Borg.
2373 Earth after the ENT-E crew repairs the damage and removes the Borg timeline we the audience and the crew of the ENT-E saw at the beginning of the movie from existing.
It cannot be a predestination/pogo paradox that the Borg would both succeed in assimilating Earth and fail at assimilating Earth. If it was just one timeline that was being rewritten, however, then that could work.
The same way how Trouble with Tribbles and Trials and Tribble-ations can exist. TWT happened originally.
Later, thanks to time travel shenanigans, this became the new history.
Third
Finally the shenanigans of the final chase of "Relativity". Where Janeway and Seven have to go through multiple points in time to arrest 3 different versions of Captain Braxton. None of it makes sense, but the action is flowing, so the audience doesn't think about the logic and dialogue characters are exposing.