I think we dodged some major continuity-missiles here tonight (unlike the unfortunate planet at the very end of the episode), and of the very minor stuff, I really didn't see much of anything that future Litverse MU stories couldn't theoretically "spackle" over to make fit if they had to, even the Empress-reveal.
Even the Mirror Klingon Empire as depicted in this episode seems to be in shape to end up where we see it in The Sorrows of Empire -- evidently not yet fully conquered by humanity, with Mirror Voq talking about how the Great Houses were still struggling to recoalesce (just as in the Prime Universe), and I can easily see Mirror Gorkon picking up the pieces down the road, assuming future episodes don't contradict this further.
And yup -- assuming that Sarek survives, what happened on Harlak could hypothetically be viewed as suppressing his future desire for revolution (and explains why he tries to talk Mirror Spock out of his plans in David Mack's novel). The big thing is whether or not his "hidden" identity gets revealed ("The Fire Wolf"/"The Prophet"), since he basically holds a high-ranking position in the Vulcan government by the time period of "Mirror, Mirror" and David's book.
As you mention (and last night, I re-read "Ill Winds" just since I hadn't done so in awhile), there's quite a decent chronological gap, relatively-speaking, between Dayton and Kevin's story and these episodes, and IIRC, there was nothing potentially contradictory to Discovery (at least, as of tonight) in their Shards and Shadows tale either, so some bridges can probably be built, here.
But, yeah, there's still next week to go, so we'll see what happens.
