Great thread,
BillJ!

I agree with all your points. I'll add a few of my own, although they're more on the nerdy side...
Earth
It's amazing. I've always wanted to see busy cities in Trek's world, but of course they could never afford to show more than sleepy back streets and a tranquil academy campus. Yes, it's not much different from the world's of other futuristic sci-fi blockbusters or ours today, but I love it nonetheless - and it's implications for the rest of the Trekverse. Picard stuck in traffic or Worf waiting for a bus is at once ridiculous and awesome.
Also, no nudist parks where kids take their pet tigers. Always a big plus.
The details
Even the virtually illegible background graphics and signage tell a story. There is an insane amount of detail, and none of the endless anime or Buckaroo Banzai references that typified TNG-era screen graphics (in a movie featuring Buckaroo himself, no less!) It's all Star Trek, drawing on a half-decade of rich backstory, and goes a long way to making the world feel alive. Newscasters talking about unrest on Andoria and culture clashes going on across the sector, damage report graphics referencing technology detailed in
Mr. Scott's Guide to the Enterprise. I've had far too much fun spotting them all. It's another whole layer of fun for hardcore Trekkies.
Nerdy questions answered
-Endless debates about continuity of timelines settled (officially, at least) by a display of Trek models on the Admiral's desk.
-Remember "The Immunity Syndrome", where Spock felt the sudden death of 400 Vulcans? Turns out he felt those 6 billion die in ST'09 too.
-Khan is shamelessly from 3 centuries ago. No attempt at retconning Trek into our world, they embraced Trek as a universe unto itself.