Continuity, schmontinuity. It's all about wish fulfillment. Mine.

Making stuff look cool with state-of-the-art fx is not a continuity error, any more than suddenly changing a show from black and white to color is. Introducing a character’s never-before-mentioned sister is not a continuity error, any more than any backstory revelation is. A new look for a known alien is not a continuity error, any more than having a character played by a different actor is. I see no reason to insist that Disco is set in the Kelvin timeline.

A true continuity error directly contradicts something we’ve been explicitly told to be true. It’s not just new information never before mentioned, and it’s not a look-and-feel change, no matter how substantial. I have a lot more problems with Disco’s intraship beaming, which TOS explicitly established as very risky and therefore not done, than with Burnham's backstory or hairless Klingons. And as soon as they give me some technobabble that supposedly resolves it -- even if it's not terribly plausible -- I’ll be satisfied. Even if they don't, I'll hand-wave it, because it's pretty trivial. I don’t want to watch something excessively constrained by production values established a half century ago, and I don't care if poetic license is taken, as long as it makes sense within the current story and can pass a very cursory sniff test. I don’t want writers with creative, entertaining, thoughtful ideas to be hamstrung by slavish adherence to every picayune detail of canon.

If that doesn’t work for you, fine. A bi gezunt, as my grandmother would have said. You’re entitled to find Burnham's backstory unlikely and inelegant, or to feel that you're being asked for too much suspension of disbelief in accepting that the Discovery predates the Enterprise. But these issues are kind of like farfetched plot twists — like when a character in a novel discovers after 800 pages of hardship that his troubles are suddenly over because the relative who was mentioned in passing in chapter one just left him a fortune. Not impossible, but not naturalistic storytelling, either. Might not be your cup of tea, but it has its rewards. Yes, a high degree of adherence to continuity — actual continuity — helps bind Discovery’s story into the larger Star Trek universe. But a certain amount of poetic license allows Discovery’s story to be new, exciting, and worth telling.

Meanwhile:

• There's only one thing I want out of life right now -- and that is to hear blissed-out Stamets call Lorca "Herbert." PLEASE let this happen. Oh god PRETTY PLEASE let this happen. That would be incredible.
• And while we are catering to my fantasies, I want another Disco party with cameos by Claire Danes and A.J. Langer playing beer pong with Wilson Cruz.
• Something I look forward to: When Tyler is revealed as a Klingon spy and Burnham is crushed — and Tilly gives her a hug.
• I’m not sure how long it’s been since Admiral Cornwell was captured by the Klingons, but it seems like a fair bit of time has passed, and that’s…disturbing. Is Lorca really such a dick? Does it actually take that long for Starfleet to issue orders? The preview promises to return to that story next week, and I hope this is not as foul as it seems.

Also:

Burnham: I wasn’t attempting to be rude. It’s just that my experience with parties is limited.
Tyler: Easy Burnham. I get it. The Vulcans don’t party? What about the Shenzhou? You served on her for what, seven years?
Burnham: Due to my rank, interpersonal fraternization was not appropriate.

So apparently Sarek turned up on the Shenzhou, said, “This is my ward, give her a job,” and they instantly made her First Officer.  ¯\_(ツ)_/¯