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.
Imperfection - S7-E2
Continuity mistake: Tom Paris is already wearing his wedding ring in the scene where he is assisting the Doctor with Sevens operation. He doesn't get married until the next episode.
Continuity mistake: The registry on the shuttle that brings Paris to Voyager keeps changing between "NCC 71225" and "NCC 1701-D".
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: 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: When Neelix shows Torres her own quarters, her bat'leth can be seen in the background. It's a run of the mill bat'leth, unlike the one she actually hung up in 'Prophecy', which was gunmetal and had a spike in the middle.
Continuity mistake: When Tuvok and Paris go scouting the holodeck, Chaotica's fortress is visibly damaged, but in a later shot when Kim and Seven are looking at it from astrometrics, the building looks like it's completely intact.
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: When Tom explains to Alice why he can't leave the Voyager, he has a three-day beard. Later in the ship, when Alice convinces him to turn on the neurological interface, he is cleanly shaved. But in the next scene he has his beard back again.
Continuity mistake: Paris reports that several ships have dropped out of warp off of Voyager's port bow, but when the ships are put on screen, they are approaching from starboard aft.
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)
Continuity mistake: When future Kes is talking to Neelix in the kitchen, when he says he's already reserved the holodeck, he's holding the smaller container. In the next shot, the smaller container is on the counter and he's holding the bigger pot.
Continuity mistake: When Seven and Naomi are playing Kadis-Kot, the pieces on the board and on the table change after Seven wins in the next shot.
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 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: 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: 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: In the scene where Tuvok is performing the meld Seven of Nine's hair is noticeably out of place as a result of struggling in the restraints, yet just after the Vinculum is deactivated it is neatly back in place. (00:38:15 - 00:42:50)
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: 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".
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