Also, if you’re going to have a tactical strike force (which is not wholly a bad idea, even if Enterprise used it) they should have something more advanced than “black” uniforms. What looks black visually to us is not black in other areas of the EM spectrum. You need actual refractive camouflage, in as many wavelengths as you can manage.
I’d hew to the idea that this is a naval vessel, & sometimes characters get re-assigned. At some point Sulu would get his own command. And I’d probably fold in some elements from Enterprise, like most Vulcans (the ones who weren’t raised by human mothers) finding humans odd-smelling, & there being a couple of noticeably different periods in the dominant Vulcan culture since Vulcan went spacefaring (Enterprise’s surly Vulcans versus the almost mystical telepaths like Spock).
Also, I would have a villain named Geoffrey Jacob (“G.J.”) Abrahams.
In a similar vein, I’d fully explore the consequences of the technology as it was depicted. The transporter was shown to have so many one-off, near-miraculous/disastrous applications- cloning, filtering out disease, reversing old age, travel to alternate dimensions (were any of the time travel eps transporter-based?), and so on. What if someone fully exploited this technology for their own purposes?
Actual warfare in the ST universe with that level of tech would be far more devastating. There were a lot of ways an enemy could destroy a planet pretty easily. Why wouldn’t the Romulans or Klingons just send a few cloaked ships smashing into the Earth at max warp? Why did no one ever try to recreate the Genesis device to use as a weapon? One TNG episode had a ship casually destroy the entire atmosphere of an uninhabited planet in about five minutes just to keep the Enterprise from finding something there.
Hire Bruce Lee as a fight choreographer. Five minutes of his time could have improved this. I’d say write him a part, but I wouldn’t want him to overshadow the cast ala Green Hornet.
No, but he’s always revered the idea of the south, with his ol’ time genteel semi-Foghorn Leghorn affectations - “Ah, say, ah, say, ah’m a doctor, not a bricklayah”. He could have an interesting episode in which he gets to see how truly nasty the south used to be, in contrast to his antebellum fantasies.
He ain’t going to be meetin’ alien babes up in the sky.
Why not take a page from the Aubrey books and have Sulu command a captured Romulan or Klingon ship, first in convoy with the Enterprise, and then back to Federation space.
Hmmm. This is intriguing.
Keep the Big Three and their relational dynamics. Keep Yeoman Rand (fix her addiction issue in RL), so that there is some sexual tension ongoing, rather than Woman of the Week + Kirk (but have that, too). Throw some female aliens and crew at Spock (an indiscretion with Uhura early on?-add some tension on the Bridge) and Bones. Scotty gets no women, period. Guy’s a complete dork–women smart enough to go into space know a dud when they see one. Give Uhura and other female crew real roles, not just reactions to the Big Three. Throw some man candy in there too.
OF COURSE the Big Three have to beam down–the show is about them, not the damned Red Shirts. Mix up the Red Shirt stuff, of course–maybe even throw in some mutiny or treason (more than has been done)–make a kitchen worker a spy or something etc.
Kick Sulu off the Enterprise. If there is justice, he is forced to serve with the Bearded Vulcan, in that world. (I can’t stand Sulu, except when he’s under the influence of whatever it is that makes him fence).
Vastly improve the special effects and hire a new costume designer, PLEASE. Keep a solid writing staff and allow them to be bold and go where–well, you know.
Keep the science real to its world. I don’t mind dilithium crystals, but keep their properties consistent. Same with star dates, warp speeds and security codes etc.
It might be interesting to play more with the Klingon conflict as a parable of the Cold War. The United Federation of Planets is pretty clearly a human-dominated but nominally democratic system, with a heavily socialized economy. Maybe give the Klingon Empire an ideology that could be genuinely appealing to at least some ordinary people in the Federation, and show the Enterprise dealing with that in some morally ambiguous ways.
For example, the Klingon Empire could espouse a higher degree of autonomy for member worlds, or greater status for traditional elites, or something along those lines. Sure, they’re referred to as the Klingon Empire in TOS - but they might not refer to, or even necessarily think of themselves, in that way. (Soviet officials always took care to refer to the USSR’s interests and goals, at least in public - not “Russia’s”.) And the Enterprise could be tasked with monitoring pro-Klingon demonstrations, or Kirk could have a drumhead trial for a suspected Klingon sympathizer amongst the non-human crew.
Overall, I’d like a clearer picture of Federation society, Klingon society, and the sources of tension (and attraction) between the two.
take a hint from TAS and get some actual Sci-Fi authors to write for the show. (Make the stories good, tho.)
Do NOT hire DC Fontana.
Keep the Holy Trinity intact.
More Orion slave girls.
Avoid moralizing. That dates a show more than costumes and hair.
Get Yeoman Colt back.
Market a real life version of tranya. ha ha ha ha
Redjac!
A scimitar? Where the hell did she keep it? Oh, that’s Ms. Baker.
Yes, it was.
What? The “bricklayer” scene doesn’t have anything resembling a Southern accent. You have to dig a ways into McCoy’s speech to find a phoneme here or there that does.
Anyway, your… point is ill-served by the confusion of the Jim Crow and antebellum periods.
Sounds like someone injested some Heinlein.
Agreed.
Shows that provide moral answers are boring.
Shows that raise moral QUESTIONS are fascinating.
If they go to the farm planet with the spores that made Spock happy, and Kirk destroys them, he should be hunted as a criminal to the ends of the universe.
That might not be too bad if they sped up the film by double. 
Get Scotty an accent coach.
Not to mention they are always alluding to sidearm phasers being able to “take out an entire room” or kill thousands of people. I’d like to see that. Furthermore, I’d like phasers to not be the nice clean weapons that makes bad guys and Red Shirts conveniently disappear in a blinding flash of light as if they never existed. I want the “kill” setting to slice people and limbs and heads like a bandsaw of light. And I want the “vaporize” setting to explode people into a bloody red mist like those cool Tesla guns from District 9.
Oh, another thing: It’s supposed to be Space, the Final Frontier. *Not *time. Keep the time travel to an absolute minimum, if at all.
Oy. The only point I was trying to make is that McCoy is a southerner, and identifies as a southerner, as well as a curmudgeon. It would be interesting to see him in the south back in the bad times.
The bricklayer line is simply the only McCoy line I could recall of the top of my head. I realize that a Horta is not an southern organism. I’m a doctor, I was raised in the south, I am far from home, and I am not a bricklayer, so perhaps I was projecting.
Redo Arena more like the original Fredric Brown story and less like Gene Coon’s vision. I’d like to see something closer to the original battle – no stupid gunpowder tricks. And, in the name of “more guts”, I want to see the original ending, not the one they used for the show.
For that matter, redo The Cloud Minders with the original script. Gerrold has written passionately about how he hated the rewrite.
I wouldn’t improve the special effects, as specified in the OP, but I would upgrade the set design. I have a blog post about it when I made a CG model of the Enterprise Bridge (original and my new version).