There's a ton of baggage I'd like to see discarded if Trek were rebooted from scratch, all the stuff rooted in the '60s origins of the show and the earlier pulps that influenced it. The human-centrism, the predominance of characters from Western cultures with names of mostly British or Irish origin, the abundance of humanoid and human-appearing aliens, the lack of genetic engineering and transhumanism, the rarity of sentient or superintelligent AIs, the lack of advanced materials and molecular engineering, the inclusion of psi powers, etc. I'd also ditch the tendency to create new random aliens-of-the-week that are never seen again, and instead put more effort into developing a more limited pool of races and building a more cohesive picture of the Federation's members and neighbors.
Oh, and a more coherent treatment of sensors. No more treating them as something separate from visual observation (e.g. "We can see it but sensors don't register it"); surely sensors would include telescopes. Anything in the open on a planet surface could be directly, visually observed from orbit, as spy satellites can do today. No "sensor interference" would prevent that unless it were actual opaque clouds or something. Also, "sensor range" should be effectively limitless, allowing only for resolution and lightspeed lag; there are no horizons in space. Eventually, powerful enough telescopes should let us image and map alien worlds from parsecs away, so no more stories where the characters know nothing about a star system until they reach it. (And no more falling out of orbit when the engines go off. The Moon doesn't need engines. Orbit isn't powered flight.)
Holodecks were a late add on, and seem to make little sense relative to what we now understand as a more likely version of VR.
I'm not so sure about that anymore. I've read that there are some fundamental limitations to something like VR goggles or the Oculus Rift or the like, since our eyes are always going to focus differently on a close-up image than a distant one, so a close-up image pretending to be distant is always going to confuse the brain. Also there's the time lag between when we turn our heads and when the VR updates the image to follow, which can be made smaller but not eliminated entirely. So that kind of VR may never be perfectly convincing or comfortable, and could cause motion sickness or the like for some people. The same could conceivably go for direct sensory induction, since there's going to be a difference between what you're made to see/feel and what your body actually senses about its environment. So that would only work if your perception of reality were completely suppressed and overridden by the illusion, and that could be potentially hazardous.
So it might be that, once the technology is available, something like a holodeck would be a better, more convincing alternative than the kinds of VR you usually see in fiction.
Transporters on the other hand are much more an issue of production. Obviously craft launches and landings would of been too expensive without, however at this point seems to be a needless part of the show.
EDIT: Be clear I'm not completely against transporters I just think they have been over used, and often get in the way of more interesting possibilities.
If I did keep transporters, I'd ditch the dematerialization angle and make them wormhole-based. That would be simpler, more plausible (to a degree), and closer to how they're generally depicted as working anyway.