Continuity mistake: The Doctor incapacitates B'Elanna to prevent her from fixing his subroutines. While unconscious, he looks at her from afar with evil intent. When he looks at her from a distance, her arms are along her sides. After the commercial break when he comes up to wake her, her hands are folded across her chest. (00:25:40)
Revealing mistake: Tuvok is behind a forcefield in Sick Bay, with the Doctor, Kes, and Captain Janeway looking at him. He tries to break the forcefield and is rendered unconscious and thrown to the floor. Janeway and the Doctor rush to pick him up and put him on the bed. Before they start to pick him up, he lifts his head and starts sitting up (to assist them, not because his character is conscious). (00:38:26)
Continuity mistake: The array surrounding the micro-singularity is shown collapsing twice, once when weapons fire causes Voyager to lose control over the anti-thoron radiation it is emitting and again when Voyager is attempting to beam Seven of Nine and Tuvok off the Hirogen ship.
Live Fast and Prosper - S6-E21
Other mistake: As Captain Janeway enters engineering after her sonic shower incident you hear crew members calling out problems on the ship. One mentions something about Deck C and another mentions a problem on Deck 22. Letters are not used to designate decks and there are only 15 decks on Voyager. (00:06:30)
Other mistake: On the planet, as the camera looks at the Harojan from behind, the zipper for his costume is visible.
Continuity mistake: When Seven takes the mobile emitter off, it alternates position a few times. First, it's right side up. Then upside down in the close up, then right side up when the Doctor appears.
Repression - S7-E4
Continuity mistake: In the theater, the assailant's hand goes from a few inches away from the Tabor's position, to touching Tabor's position.
Revealing mistake: As Icheb's parents turn their faces towards the sun to look at Icheb, the edges of the prosthetics used for the ridges on their noses are visible.
Continuity mistake: When Harry uses the scanning tool, the lights alternate between flashing from top down to bottom up and back between angles.
Revealing mistake: As Seven starts to explore, there's a flashlight floating next to her. There's no atmosphere, therefore no breeze, but it's slightly moving before she touches it.
Revealing mistake: As the camera looks into the Jeffries tube, it's easy to tell that the view beyond the second bulkhead is a matte painting used to extend the set.
Revealing mistake: The line on the make up on the isomorph is easily distinguishable.
Revealing mistake: In the basement, when the camera is in a close up on B'elana's face, the edge of the prosthetic at the left side of her hairline is visible.
Continuity mistake: When Torres and Paris enter engineering, the warp core is dark showing that it is offline. Minutes later, it is illuminated and online. (00:19:15 - 00:28:30)
Resistance - S2-E12
Continuity mistake: When Caylem dies in his close up shot, his head falls to his right shoulder, but in the next shot showing Captain Janeway holding him in her arms, his head is angled to his left (away from the camera).
Continuity mistake: When Janeway and Neelix chase after the mysterious figure moving away from the down the dead end corridor, the wall is lit up, and the shadow moves across it showing direction of travel. After a quick cut, the wall they approach, and the corridor is noticeably darkened.
Parturition - S2-E7
Revealing mistake: On the bridge, as Tuvok monitors and reports on the pursuing ship's weapons, you can see what looks like a wristwatch on his right wrist as he works the controls. (00:35:35)
Dreadnought - S2-E17
Continuity mistake: Dreadnought states there are fifteen priority targets approaching. On radar sixteen Rakosan ships are displayed. Then just before the Dreadnought attacks (and destroys three of) the approaching ships, there are a total of nineteen Rakosan ships displayed on radar.
Repression - S7-E4
Other mistake: In the 3D cinema scenes in the Holodeck, Tom Paris and B'Elanna Torres can be seen using blue/cyan anaglyph glasses and the movie screen can be seen to be in blue/cyan also. This is fine and to be expected. However the shot in which the projection room can be seen behind the couple show the projection is through magenta/green filters. (00:03:30)
Other mistake: They show Kes as a baby but her ears are human. (00:42:25)
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