Very minor thoughts about the President of United Earth:
I don't like that the writers decided to make the leader of United Earth a president instead of a prime minister.
This isn't really a continuity issue, because it's been a thousand years and United Earth could easily have developed a new constitution since then. But ENT S4 established that the United Earth government official in charge of establishing the Coalition of Planets held the title of "Minister," and that strongly implies that United Earth in the 2150s used a parliamentary system.
The post-finale ENT novels went with this, and established that the real leader was the Prime Minister of United Earth, with the President of United Earth serving in a mostly-ceremonial role, akin to the Federal President of Germany and the Federal Chancellor, or the President of Barbados and the Prime Minister of Barbados. This is a totally subjective thing, but I would have much preferred it if the DIS writers had gone with that -- if Stacey Abrams had cameoed as the Prime Minister of United Earth rather than the president.
In fairness, it does occur to me that the writers were careful not to establish explicit details about the United Earth government. In "... But to Connect," General Ndoye says only, "We recently elected new leadership" rather than explicitly saying the president was popularly-elected. And the things we see the U.E. President do in "Coming Home" -- assisting in the evacuation, arriving aboard Federation Headquarters to meet with the Federation President to announce U.E. is rejoining the Federation -- are the sorts of things that a mostly-ceremonial president might do. So anyone really attached to the parliamentary system could probably still interpret DIS S4 as allowing for a Prime Minister of United Earth.
(For that matter, someone who prefers the French or Swiss systems could interpret them as possibilities too.)
Also, I just feel a little presidented-out. In the past month, we've gotten the President of the United Federation of Planets, the Vice President of the United Federation of Planets, the President of Ni'Var, the Vice President of Ni'Var, the President of the Confederation of Earth, and now the President of United Earth. That's a lot of presidents and vice presidents! Six of them -- it's unpresidented!

I understand the desire to use shorthand that's commonly-understood by the intended primary audience, but I do think having so many presidents and VPs makes the show seem a bit U.S.-centric. Other systems of government exist! It wouldn't have been that hard to have the Federation President say, "I've informed the Federation Council that I'm joining the mission to the Ten-C. Power will be transferred to the President Pro Tempore," or to give the U.E. or Ni'Var leaders different titles.
Again, this is purely a matter of subjective aesthetics. It doesn't
really matter. But it's not quite to my taste.