Goofs

Since time travel is fictional, any "goofs" related to the functioning of time travel are purely speculative.

As is the case with many fictional depictions of historians, Lucy is treated as if she had encyclopedic knowledge of huge swaths of history. In reality, Lucy would have very deep knowledge about her specific subject area, but only moderate levels of knowledge about other times and places, particularly of things which were far away, geographically, temporally, or thematically, from her area of concentration.

An enormous plot hole becomes obvious in the very first (pilot) episode: if history has changed so much that the main character's sister does not exist anymore, then her historical expertise, which is the reason she is on the team, has suddenly become useless. She is no longer the expert, other people will know more about the new time-line than she does.