They have phasers with enough power to boil the oceans of a planet, and torpedoes that can travel faster than light. Yet every conflict takes place at extremely close proximity, often on the same plane, as if they were ships in the age of sail.
They have force fields with a critical flaw (harmonic resonance means any energy weapon using the same frequency as the shields can just shoot right through them) but whenever this is even mentioned, the shields have to be re-adjusted manually.
Unauthorized people can appear on the ship, and crew can vanish from the ship, and the computer either doesn't notice, or does and never alerts anyone or activates any sort of countermeasures. The first officer can be sucked into a pocket universe and have his organs rearranged by non-Euclidean bug monsters and no one will ever know unless they happen to ask the computer where Riker is at the moment.
It's been established that transporter buffers can be used to "back up" a person, even long term (in the TNG episode "Relics," Scotty is discovered having stored himself in a transporter buffer for decades with no ill effect.)
Replicators can't do latinum and living tissue, but they work by literally converting energy into matter and assembling it into something atom by atom. At that resolution, there's no difference between anything and anything else, so there's no reason why replicators shouldn't be able to replicate anything.
The former two items, along with the holodeck (which can create sentient life on request, BTW) should guarantee that no Federation citizen ever truly ages or dies, or even ever has to exist in a physical body. The Federation should be a post-human, post-singularity society. Yet for "plot reasons," none of these glitches (like the transporters being able to clone people simply by refracting the transporter beam) are ever harnessed for their real potential.