Everyone's saying the SFX would need to be re-done because they're 480i — but couldn't they be interpolated up to HD resolution?
Many of the most commonly used effects (such as transporter beams, phaser shots or replicators) probably wouldn't look that bad upscaled, since they weren't sharp, clear images to begin with, they were only misty swirls. Also, all the replicator and transporter effects look really quite nice even by today's standards, and don't need any kind of updating in terms of style.
Having said that, I would really, really
love all the SFX to be re-done in HD. I was watching an episode last night and imagining how beautiful the space scenes would look if they were re-done. They could add so much to the episodes.
Could look amazing with a (well done) CGI Enterprise and some nice new phaser effects and better explosions, with some more adventurous new camera angels to give more drama, and with a lot more movement of the ships.
A lot of the matte planet shots could be greatly improved, if only by cleaning them up, blending them better with the live action, and making the camera movement more natural. (And a touch of animation such as moving water, birds, or little people walking around.)
As for the space shots of planets, they really need to be completely re-done. At the time, they were good. They're still good. But they can do so much better planets these days.
I don't normally believe in adding things that weren't there in the first place, but I would actually really love them to 'modernise' the holodeck effects, so instead of characters just disappearing with a fade, they do that really cool effect that you saw the EMH do in Voyager, where the background is displaced. I adore that effect. (I wouldn't object to the sound effects being 'beefed up' a bit, too). I think they cold possibly make every holodeck effect look a lot better if they used some more modern techniques.
By Voyager, they had got so good at holodeck SFX, they were even changing the lighting of the actors as the environment changed around them (a really effective trick). It would be great if they could digitally reproduce this effect. So, when Picard ends the Dixon Hill program, instead of the lighting on him not changing at all, they could match him more with his respective background by having the brightness/colour levels change accordingly, and the effect could look really good.
I would hope to see a lot more streaking stars out the window instead of the static starfield you normally saw, even thought they were sometimes supposed to be travelling somewhere. I can only really ever remember one shot of streaking stars out a window that also had camera movement (it was in ten-forward). It looked great, and I'd love a lot more of that. I'd also like to see the planet they're obiting out of windows, or seeing the top of the nacelles in the distance from the observation lounge window.
Something they absolutely must not do
is get rid of the reflections in the glass. It would be a very cheap way of adding window exteriors (stars and planets), but the apparent lack of glass would also make it look less realistic. Therefore, all the reflections should be kept, and added over any new exterior graphics. This would take quite a bit more work, as they will have to remove stars that overlap outside objects. Although they won't have to remove stars when adding moving/streaking stars, because there are always some static ones in the background anyway.
How 'modern' can they go?
Where remastering TOS, they had to be really careful not to go too far and make it look too mordern (because it was a 60s show and overly modern effects would look out of place). However, with TNG, the series ended only just over 10 years ago and progressed into movies that have only just finished. So I don't think it needs the same kind of careful 'historical preservation' treatment. I think most TNG fans want it to look really good and modern, because to us TNG is a modern show.
For example, if they could make the Borg in season 2 look and sound like they did in First Contact (ie a lot more menacing), I would be all in favour of it. Modifying a show to make it more consistent with what it always strove to be (and ultimately became) is acceptable.
I know some will disagree with me on this, but I think I have the right to my opinion, as I grew up watching TNG and I love it dearly. I am a big fan, so I feel any TNG:R would aimed at people like me. (I can't say the same about TOS because I didn't grow up with that show.)