Visible crew/equipment: When the camera turns to face Tuvok as he approaches the crazed Hirogen, two stage crew members can be seen at the left side of the screen. The first is a rather plump man wearing what appears to be dark pants, and a short sleeve light shirt, while the second is squatting down in front of the first wearing shorts. (00:09:05)
Visible crew/equipment: After Paris hails Tuvok about the problem in the mess hall, a brawl breaks out. When the new Hirogen Alpha enters the galley to access the com relay, just as this Alpha removes the front panel in order to transmit a signal, the actor's green tape mark is visible on the floor. (00:39:00)
Other mistake: On the planet, as the camera looks at the Harojan from behind, the zipper for his costume is visible.
Answer: If you include the original Star Trek series (1966) then there are several. The communicators used in the original series were before (and said to inspire) mobile phones. We currently do have teleportation technology but it currently only works on things the size of a few molecules. A "Cloaking device" also exists; it's a fabric that bends light through it, though it currently only works in infra-red. The Hypospray is real and was patented in 1960 - six years before the original series aired - it's actually called the Jet Injector. Faster Than Light travel is still a few decades off, but there are several real-world theories that look promising, including one that is remarkably similar to the method used in the Star Trek Universe called the Alcubeierre Drive that involves manipulating spacetime ahead and behind the ship and the ship "riding" it. Medical techniques and technologies have also advanced considerably; prosthetics particularity and we routinely have robots performing surgeries where absolute precision is needed. The "Shield" used in the series have a few primitive versions around. The Phasers used in the series are used but are not very powerful (nor will they ever be as powerful as the Star Trek version the laws of physics gets in the way) but rail-guns (using magnets to spin then propel a projectile) and particle accelerators like the Large Hadron Collider have been around for a while. The Replicator would require a nuclear fusion reactor and a nuclear fission reactor in something the size of a large oven and the Holo-deck wouldn't work at all based on our current understanding of physics so those are both still science fiction at the moment, but who knows!
Sanguis