Continuity mistake: In episode Revulsion (Season 4 episode 5), commander Chakotay says that Voyager's astrometrics laboratory hasn't been updated since the ship left space-docks. In later episodes it is stated that Voyager didn't have an astrometrics when it was built. In Shattered (season 7 episode 11), Chakotay time-travels back to the day Voyager leaves for its first mission and tells that times Janeway that they are going to the astrometrics, to which Janeway comments, "Voyager doesn't have an astrometrics".
Continuity mistake: Tuvok and Paris' rank seems to skip around during the first season. Despite being listed in the credits as 'Lieutenant Tuvok', Tuvok starts the show as a Lieutenant Commander, with the signatory three collar pips, one black and two gold. At certain points, however, he is seen with only two gold pips (signifying Senior Grade Lieutenant). After season one he remains a Lt. Commander with no reason for the lack of continuity offered. Similarly, Paris starts the show as a Senior Grade Lieutenant, but sometimes instead of two gold pips he has one gold and one black, the signifier of a Junior Grade Lieutenant. After season one he is always presented as a Junior Grade, excluding his brief demotion to the rank of Ensign in a later series.
Continuity mistake: The registry on the shuttle that brings Paris to Voyager keeps changing between "NCC 71225" and "NCC 1701-D".
Continuity mistake: In sickbay, when Kim tells the captain he's analyzed the tricorder, the tricorder is open. In the next shot it's closed.
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).
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.
Continuity mistake: When Samantha is holding her baby while the captain talks to her, her hands are apart with her right hand under the baby. In the next shot, her right hand is on top of her left hand and not under the baby.
Continuity mistake: After Starling is beamed out of the limo, Rayne opens the door and escapes. The door is still standing open when the chauffeur starts the car. But in the reverse angle as he drives away, the door has closed itself. (00:20:10)
Continuity mistake: As Starling prepares to launch the timeship from the bay behind his office, there is a shot of the exterior of the ship. In the background of this shot, there is a white wall on the right. This wall carries the company name and logo. However the name is misspelled here as Chronowerks, instead of Chronowerx as was shown on the outside of the building and behind Starling and Janeway when they were in the office.
Continuity mistake: The sun's location changes when Rain and Tom are in the stalled van. After Tom shoots the truck and Rain stops the van, you see the shadow is directly under the van. When the truck is heading towards them, we see the van's long shadow across the highway, to the right of the van.
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.
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)
Continuity mistake: Tuvok announces to the bridge he has detected a "polaron grid" surrounding the planet Voyager is orbiting. Minutes later, Chakotay tells the Captain that they have found some small holes in the "tachyon grid". (00:25:50 - 00:29:30)
Continuity mistake: Through the series, it is stated several times that Voyager has three transporter rooms, like in Phage (season 1 episode 5). However, in this episode, Voyager suddenly only has two transporter rooms.
Continuity mistake: As Janeway calls the bridge after a conduit is blown out by Kes, her combadge is askew. A moment later when they meet Tuvok, it's correct.
Mortal Coil - S4-E12
Continuity mistake: The shuttle is "parked" in the nebula to get a protomatter sample, and the nebula is visible in all windows. After the shuttle is hit, the camera looks at Tom, and the view in the window is the black of space with stars, rather than the bright nebula.
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.
Continuity mistake: When Seven gives her log entry at the beginning of the episode, she lists the Star Date as 15781.2. This is a misstatement of the correct star date, 51781.2.
Continuity mistake: Early in the episode, the Kyrian historical researcher plays a simulation of events aboard Voyager that include Janeway killing a Kyrian and then throwing the rifle to a crewman. Later, he replays the simulation for the Doctor, but subtle details of this 'same simulation' change, most notably the way the female crewman raises her rifle much sooner the first time we see Janeway walk past her, and the difference in the way the male crewman catches Janeway's rifle. (00:14:15 - 00:26:20)
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