Laser eyes?!
I think one thing star trek was sorely lacking in was realistic technology development. I give as examples drone fighters, personal shields, EMP beams, holograms, nuclear weapons, and multiple warp cores per ship.
Drone Fighters: there was a race in a star trek video game that used these. They were kinda lame, but that's not the point. Starfleet could totally have used them. And the Enterprise was always using probes and loading up shuttles with interesting remote control stuff.
Personal Shields: remember the NG episode with Worf stuck in the wild west holodeck program? He (a non-technical person) rigged a personal shield that deflected one or two bullets using primitive hand tools and powered by his communicator battery. What a trained scientist with replicators could do would be astounding.
EMP Beams: a volley of phaser fire tears apart your forward shields, and a sudden invisible blast from the same ship disables your ENTIRE ELECTRICAL SYSTEM. Joy. Okay, I know why nobody ever puts these in, they're overpowered. But you know they would have developed them.
Holograms: why beam down to the planet for diplomatic negotiations when you can send a hologram? Are they offended that you think the place is too dangerous? Of course it's dangerous! They KNOW you know it's too dangerous and you don't want to be trapped there.
Nuclear Weapons: An explosion in space is different from an explosion in an atmosphere. But the energy output of a nuclear weapon is too great to ignore. If missiles with conventional payloads can damage ship shields, then missiles with nuclear payloads would blow away a station's shields and tear it apart, irradiating it forever and killing everyone on board with one shot. Oh yeah, overpowered and not convenient to the storyline.
Multiple Warp Cores: One ship has one warp core. This core powers the warp engines and miscellaneous other stuff. When the ship drops out of warp, it has tons of extra power to spare for things like shields and charging phaser capacitors. Why not just stick three more warp reactors in there? The power can be dedicated to shields for one, weapons for another, warp power for a third, and the fourth is for internal shields, transporters, communications, sensors, life support, and the bartender's vibrating chair in ten-forward.
TL;DR: I've just geeked out and I'm sitting here panting :/