Chief among these is the players' (and GM's!) historical insecurities.
History is a BIG subject, and few gamers will be experts. Even History majors will have their niches. One player might be very familiar with World War II, but be very weak on the Napoleonic era or Antiquity. It's just too broad and deep a tapestry, ESPECIALLY if you're going to play around with the threat of CHANGING history. Like, how do the players know the Chinese explorer Zheng He was meant to lose governmental support before he could go too far? How do they even know who Zheng He WAS?!
How a GameMaster handles holes in both his knowledge and his players' really depends on whether they are history buffs or not.
First, the GM should be ready to accept the word of Historians whose specialty lies in the chosen period and revise the details of the setting/scenario in line with comments from the table, even if reality must be "edited" after the fact (unless of course, the change is willful on his part and a designed element of the story, what "needs to be fixed"). There's no shame in admitting one's ignorance, and the session becomes a collaborative learning experience for all concerned.
Second, Historians are really very good at research and you can capitalize on that. Everyone's got the Internet in their pocket these days anyway - in other words, this tip will also work, probably to a lesser degree, with non-Historians - so let them have access to their mobiles (perhaps in tandem with a Skill roll of some kind). Historians might well be able to spot a discrepancy in the timeline and will have the Googling skills to track the changes back to the historical turning point. By letting them do their own research and use Internet sources as their character's memory/database, you cut down on boring old exposition where you're forced to tell the players what their PCs know, or run them through briefings that gives a lot of their agency to higher-ups.
I'm just finishing What If? 2 right now, a book of what might have beens written by historians, and it (and the first volume) is a great resource for historian-centric time travel scenarios, detailing an alternate history the PCs might land in, and forcing the researcher in the team to track the changes back to the turning point they then must fix. Non-historians might not be as able, quick or interested when it comes to that specific kind of adventure requirement.
If no one really digs History, and they're still playing a time travel game, it's a little like playing D&D in a setting you hate. The focus must be elsewhere.
The thing about History is that it's normally an immutable "place". You might well topple an empire in the Forgotten Realms, but if you do so in History, you might very well prevent your own birth and screw the whole "setting" up. My advice? Allow it.
With non-Historians, accuracy is a waste anyway. Don't presume they have to go back home, or keep the timeline intact. Allow them to treat History as a mutable setting. They want to kill Hitler in 1935? Or buy up all his paintings and turn him into a successful artist? Let them. They want to bring automatic weapons to 50 B.C. and mow down Caesar's legions in Gaul? Sure, why not? Using History as a playground can be tons of fun.
But wait, what about the changes to history? Couple ways to go about it, really. The GM could run the setting by the seat of his pants and, analyzing what the players' actions are doing to the timeline, extrapolate a consistently evolving History that now becomes the new setting. PCs can even go back in time and prevent their own actions from ever happening while retaining memory of them, so these can be undone if they somehow trigger the "darkest timeline" and lose something dear to them. (It can be as simple as "awww, I can't go to the Old West anymore? But I LOVE the Old West", or as deep as having fallen in love with a woman from a 1659 that no longer exists.)
The other way to do it is to say changes in History create new parallel timelines. The time machine can just go back in time, then take the original branch back up through history, while still retaining the ability to revisit old parallels where they saved the dinosaurs or accidentally killed Shakespeare.
The point is to remove "historical anxiety" from the equation. The characters can still deal with "local" consequences (i.e. those that have ramifications for their characters and the people they meet and befriend), but aren't paralyzed by the unknown and unknowable (at least to them) results of their presence back in History.
Regardless of the type of player you've managed to draw in, time travel RPGs can't be about being mere observers. Oh, it might start that way, but for the game to be fun and have stakes, the PCs must become participants. Don't be afraid to bend the rules to make that happen, even if the game's are fairly clear-cut.