A lot of the ones already mentioned.
That initial zoom in to the bridge of the
Enterprise from "The Cage" is still pretty great. It immediately gives us a good look at the ship and elegantly establishes exactly where the bridge is:
https://tos.trekcore.com/gallery/albums/0x00/thecage008.jpg
https://tos.trekcore.com/gallery/albums/0x00/thecage009.jpg
https://tos.trekcore.com/gallery/albums/0x00/thecage010.jpg
https://tos.trekcore.com/gallery/albums/0x00/thecage011.jpg
I love Albert Whitlock's matte paintings for the show. In particular his rendition of Delta Vega from "Where No Man Has Gone Before" ("Nobody here but us chickens, Doctor."):
https://tos.trekcore.com/gallery/albums/1x03/wherenomanhasgone263.jpg
And Starbase 11 from "The Menagerie" and "Court Martial":
https://tos.trekcore.com/gallery/albums/1x11/themanagerie1_003.jpg
https://tos.trekcore.com/gallery/albums/1x20/Court_Martial_003.JPG
The surface of Eminiar VII is pretty great too:
https://tos.trekcore.com/gallery/albums/1x23/A_Taste_of_Armageddon_045.JPG
And I love the simple device of cross-cutting between the two
Enterprises at the beginning of "Mirror, Mirror." It immediately and clearly establishes the possibly confusing idea that Kirk and company have been transported into an evil opposite universe (At 2:09 in the video below). It's also a great touch that the Mirror Universe
Enterprise has the spikes at the end of the nacelles, while the regular
Enterprise doesn't:
And I love that shot of the
Fesarius in "The Corbomite Maneuver" where it continues enlarging past where you expect it to stop until it's positively dwarfing the
Enterprise and
Oooooh Shit our heroes are in trouble now:
https://tos.trekcore.com/gallery/albums/1x10/corbomitemanuever144.jpg
And in the non-Remastered shot...the 1701 is absolutely dwarfed and tiny by comparison.
In the remastered shot because of how they ultimately composed it; you you get the impression the Fesarius is big; but it doesn't have the same visceral effect of just HOW SMALL the 1701 is in comparison when compared to said original non-remastered shot.
As some have said above; many times the CGI artists working on the remaster seemed to not realize WHY certain effects shots were composed in the manner they were. These guys seemed to just wanted to up the visual details of the respective ships, thinking it was the issue with some of the original effects shots without considering that there was a valid and important in narrative reason to compose a shot in the way they did.
Exactly. The moments where I hate the new remastered FX (and there
are also several shots I really like) are in the places where they obviously assumed that those poor dumb clods in the '60s did things wrong and they didn't consider that there were
reasons why the original effects crew did what they did.
It looked like this... where the brightest surfaces of the Enterprise are brighter than the @#$%ing sun!
Ha!

I hadn't thought of that before, but you're absolutely right. Not getting brightness and shadows correct is a common mistake in modern FX, probably because many of the artists know computers better than basic artistic principles.