To begin with, I'm noticing that a curious number of things in Star Trek seem to operate in pairs. There are, for example, two warp nacelles; there are two different ways of getting to and from the ship, two different weapon systems, two propulsion systems, etc. I've thought for a long time there are a couple of these pairs are actually somewhat mismatched and would a lot more sense technical if you actually reversed their order. It's almost as if huge parts of the ship were actually installed upside-down and nobody noticed.
There are 6 major ones that come to mind:
It's literally upside down.
The bridge is at the top of the saucer section. while the sensors are at the bottom of the saucer. It should be the exact other way around; sensors should be at the top where they have a better view of surrounding space without the secondary hull blocking the rear aspect. The bridge should be at the bottom, where for no apparent reason starships normally orbit planets with their bellies facing the ground anyway (where, also, gravity will be pulling you if you ever descend into the atmosphere or approach close to very low to a low-gravity moon or asteroid).
Your field of view is better, and being closer to the torpedo bay (or phaser bank, see below) means you have a much easier time directing your weapons. It's also better protected on that side of the ship; there are fewer angles from which an attacker would have a clear shot to the bridge, and most would involve positioning himself within a line of sight of your main weapons.
Also, the view is probably nicer.
* PHASERS vs. PHOTON TORPEDOES
Especially post TOS, where starships have a large and complex torpedo launcher and multiple phaser banks all around the ship. What puzzles me is that there's no specific reason to have a torpedo launcher with a direct linkup to the main engines; if you're just spitting a rocket-propelled missile into space, why do you need to be close to the engine core? Moreover, TOS and TMP both imply that the ship is capable of channeling the power of its main engines directly into the phaser banks, which would seem odd when you consider the main phaser banks are nowhere NEAR the main engines. Add to that the fact that starships never seem to fire more than a single phaser bank at any given time...
Switch em around.
Stick the phasers in the torpedo deck, where they can suckle power directly from the main reactor and discharge one hell of a blast at whatever the ship is pointed at. Photon torpedoes, meanwhile, are moved into the launch tubes in the saucer section; the TMP Enterprise would have, say, eighteen different tubes each with ten reloads for a total of 180 torpedoes that can be salvo-fired to blanket a wider area. IOW, you'd use phasers to hit a single heavily-shielded target and torpedoes to hit multiple small targets that may or may not be maneuvering evasively.
TNG would have the very interesting implication that the phaser arrays would actually be a very long chain of single-shot torpedo tubes with small hatch covers, sort of like the VLS cells on Aegis cruisers. A Galaxy class starship would carry close a thousand photon torpedoes and the ability to launch every single one of them in an instant. Picture "Best of Both Worlds" antimatter spread... but with torpedoes!
* IMPULSE vs. WARP
Not the engines, necessarily, but the powerplants.
There's a fundamental problem with using antimatter as a fuel source: when matter and antimatter annihilate, their main product is a lot of hard x-rays and gamma radiation. There's not alot there that you can really use for conversion to raw energy, and it's certainly nothing you'd want to channel through a hundred meters of conduit into a pair of giant propulsion units sitting outside your ship. So unless the warp core is a device that MAKES antimatter for the nacelles to burn (which is a whole separate discussion altogether) it doesn't really make sense for the warp drive to use antimatter as a fuel source. It makes even less sense for impulse engines to use fusion reactors, since fusion could provide a VERY efficient heat engine for relatively little radiation hazard and because fusion fuel is easy to obtain, easy to replenish, and can actually be recycled by running exhaust products from one fusion reactor into the fuel cycle of a second reactor (Reactor One fuses atomic hydrogen and produces helium and tritium; reactor two fuses deuterium and tritium, reactor three fuses helium and tritium).
So switch em around.
Pump the antimatter into the impulse engines, which can now use just about anything you want (say, molten lead or some other dense metal) as a reactant mass.
A tiny amount of antimatter would produce a spectacular amount of thrust from a relatively small amount of fuel and would allow the ship to maneuver at high speeds even if its main powerplant were shut down. If you choose the right reactant mass, you can even render your exhaust non-radioactive, avoiding potential environmental hazards. Moreover, the fusion reactors running the warp drive could be very VERY efficient, chewing on the same couple of liters of hydrogen for months at a time before the ship has to replenish its supply. Secondary "afterburn" reactors reactors with a more violent fuel cycle could be brought online as needed.
* COLLECTORS vs. DEFLECTORS
The deflector "dish" is supposed to sweep debris out of the ship's path at warp speeds while the ramscoops collect interstellar gas to be processed as fuel. These two devices are in exactly the OPPOSITE places where they should be to do their jobs; to begin with, fuel is (supposedly) burned in the warp core and not in the nacelles, thus any material collected by the nacelles would have to be piped back down to the reactor to be processed and filtered, then burned in the warp core where energy is then piped back UP to the nacelles to be used for propulsion. The main deflector, likewise, is physically separated from the two most powerful subspace field generators on the entire ship and becomes basically a third wheel that can also draw power from the reactor.
So switch em around.
Make the shields/deflectors part of the warp drive. The same system that can hurl a starship through space at thousands of times the speed of light should be capable of hurling other objects AWAY from it the same manner. If the engines themselves can't be tuned to do this (and they probably can't) a deflector system installed in the endcaps of the nacelles would constitute a type of modified warp coil that produces a warp field around the ship that causes all approaching matter and energy to accelerate away from it. If you want to hit the starship with a torpedo, that torpedo would have to contend with the full power of the ship's warp drive trying to push it in the opposite direction.
Meanwhile, move the bussard collector into the "dish" on the secondary hull; it creates a forcefield in front of the ship, extending out hundreds of thousands of kilometers, into which interstellar gas is funneled and collected by the warp core (which is now a fusion reactor and doesn't need to be replenished but once every couple of months).
Significantly, you don't have to be at warp to do this; put your ship in orbit of a gas giant and fly through its upper atmosphere with scoops on. Filter the intake, sift the hydrogen, chill it down to slush; we're good for the next three hundred light years.
* SHUTTLES vs TRANSPORTERS *
Away teams use transporters to beam down to different planets to see what's down there and they only use shuttlecraft when the transporters aren't good enough or when they simply have too much crap to carry. Apart from the fact that using a transporter is INTRINSICALLY more complicated than using a shuttle, there's that annoying little conceit in Star Trek that every planet you will ever encounter is not only Earthlike, but has an atmosphere and environment so similar to Earth that you can literally walk right into it and suffer no ill effects at all, and that there is nothing poisonous/paranoid/hungry within range of the beamdown site that you might want to avoid. Predictably, away teams only transport down to the planet with whatever they can carry on hand, expecting that if they need anything else they can always call the Enterprise and either get beamed back out again or have something sent down to them. Yet this often fails to be the case -- transporters stop working, the away team gets stranded/captured/ambushed/injured, the ship gets chased/lured away by aliens, etc -- and the ground teams are stranded for extended periods of time with only the clothes on their backs and whatever was in their pockets when they beamed down.
Switch em around.
Shuttlecraft should be the MAIN method of landing away teams on a planet surface and should be fully stocked with survival gear, medical supplies, portable shelters (assuming the shuttle itself can't be used as a shelter), weapons, tools, and anything else an away team would need to explore the surface of an alien world.
In other words, sort of like these guys:
Except imagine there are, like, twenty of these and their command module is the size of a city. I also find it incredibly difficult to believe that the only strange new worlds worth sending a landing party are those incredibly Earthlike ones that can be explored without space suits or breathing gear. If the civilization you just encountered breaths a methane/ammonia atmosphere at 4.5psi, you're gonna want to bring space suits; unless you live in a universe where nothing could ever possibly go wrong with the transporters, you'd better bring the shuttles too.
Moreover, an aerial survey of the landing site should be standard procedure; scout the landscape for a mile in every direction and make sure you understand the terrain you're about to land on before you set down. Scan for life forms (carnivorous or otherwise) and track their locations, scare them off if you need to, catalog them from the air. Once you land, you'll probably want to cycle the air to match ambient local pressure and atmospheric conditions so your landing party doesn't immediately get the bends the instant they arrive (or for toxic/vacuum worlds, check your space suits and your gear one last time). Transporters seem to have an impressively long range, and thus should be used INSTEAD of shuttles to transport bulk cargo and large numbers of personnel to and from the ship.
* HELM vs. TRANSPORTER (consoles) *
You activate the transporter by pushing three sliders forward; the console has a big targeting display in the center of it that tells you where you're going, and it has other controls for automatic settings and for adjusting the beam width and intensity. Meanwhile, the helm console has an astrogator and some random buttons.
For the love of god, switch em around.
Your engines have variable power settings, the helm console should too. The transporter should not; if you want to beam someone down, have it be three buttons you have to press and HOLD until the transport cycle completes. Also, the big "location finder" on the TOS transport console is EXACTLY the kind of thing Sulu should be looking at when he's trying to navigate a 100,000 ton starship and/or aim its main weapon systems. The puny little popup viewfinder? Not so much (although it's just what he might want to use to view a telescope image of a landing site he was about to beam someone down to.