Revealing mistake: As Kurn is chastising Worf in the infirmary, the actor's prosthetic nose has become detached from the rest of the Klingon make up. You can see the nose wobbling around as he talks.
Revealing mistake: Clear use of a stunt double for Avery Brooks during the brief tussle with Dax in the holding cell.
Other mistake: As Kira is showing Ziyal the Federation rifle, the compartment underneath the rifle flips open unintentionally.
Visible crew/equipment: As the Defiant tries to contact the Ulysses, the camera pulls too far back at Odo's station, and we can see the microphone along with the boom pole above the captain's chair. (00:14:40)
Factual error: The United States conducted no nuclear tests in 1947 and conducted none in Nevada until 1951.
Plot hole: Thomas Riker is able to steal the Defiant partially because he's a genetic double for and not a clone of Will Riker. Thomas Riker's existence is not a secret. Star Fleet is aware that the first officer of their flagship has a genetic duplicate who resigned and is out there somewhere. There should be something in place to verify Will's location before giving Thomas access. But then, of course, we wouldn't have an episode.
Suggested correction: At this point Thomas Riker is still a Starfleet officer. There is no need to lock him out of accessing the Defiant's systems as he is considered just as trustworthy as Will.
It's said that he resigned over suspected Maquis sympathies. They were right.
They say that he had expressed political opinions that supported the Maquis, not that he had resigned from Starfleet. A large number of Starfleet officers supported the Maquis' intentions, but still stayed loyal to Starfleet.
No, Thomas Riker accessed the Defiant under the guise of being Will Riker, and Major Kira released the lockouts being under that impression.
Exactly. NOBODY in Star Fleet has thought "Well, what if one of them claims to be the other? How do we tell them apart?"
Other mistake: Nog is promoted to Lieutenant Commander but is given the rank insignia of a Lieutenant junior grade.
Visible crew/equipment: After Kira returns the expensive gift to Zek, when Quark kneels in front of Zek we can see the T-mark on the floor, under the table. (00:23:15)
In the Pale Moonlight - S6-E19
Revealing mistake: As Sisko is threatening Tolar in the simulator, Tolar's prosthetic mask can be seen to bend awkwardly against the wall, as if made of rubber.
Other mistake: Dax says that T'Lor (the blue-shirted alien) had the away team's only medkit, but when he was shot and killed, T'Lor only had a phaser rifle on him.
Suggested correction: Just as T'Lor is shot and falls off the runabout you can see the med kit hanging from his right shoulder on a strap.
Visible crew/equipment: After the infant Changeling gives Odo the bittersweet gift, Odo exits the infirmary and shapeshifts into the Tarkalean Hawk. As Odo soars through the Promenade's top level, we can see a director's chair beside the spiral staircase, down below. (00:41:15)
Emissary (2) - S1-E2
Revealing mistake: During the chaos on the Promenade as the Cardassians attack, a man can be seen landing on a steel girder that bends like rubber or foam when he makes contact.
Character mistake: At the end, Sisko blames the deaths of the runabout crew (Hoya, Rooney and Bertram) on himself and the Vorta not trusting each other. However, the runabout was destroyed before any negotiations had taken place, and even before any Jem'Hadar or Vorta had landed on the planet, so their deaths were largely unavoidable. Even the later deaths of T'Lor and Muniz were caused by the first firefight, again, before any negotiations had happened.
Suggested correction: Alternatively, Sisko could also be referring to the general mistrust that exists between Starfleet and the Dominion, which is constantly threatening to boil over into full scale war. Without that prejudicial mistrust and paranoia, The Jem'Hadar would have likely never killed Muniz or attacked the runabout. Indeed, it can be said both sides inability to negotiate throughout the episode is due to their mutual belief that the other side cannot be trusted under any circumstances.
The Way of the Warrior (1) - S4-E1
Character mistake: At this point in time, the Khitomer Conference (where the Federation and Klingons resolved their conflict) was at least 70 years ago, yet Bashir refers to their peace with the Klingons as having lasted two decades.
Plot hole: Just after the Kelleran soldiers kill all the scientists, O'Brien tries to contact the runabout Ganges for a beam out. Unable to contact the Ganges, he and Bashir use the T'Lani cruiser's transporter to beam down to T'Lani III. He could have used the cruiser's transporters to beam to the Ganges instead (it wouldn't have had its shields up as it was unoccupied and was closer to the cruiser than the planet) allowing them to escape back to the wormhole and DS9, instead of having to await rescue on the planet.
Factual error: When Major Kira was introducing Lieutenant Commanders Dax and Worf to the arriving Trill scientists, she introduces them as Commander Dax and Worf. While in informal conversation, they could be addressed as Commander, when making formal introductions, the person making the introductions would use their full proper rank. This is an error that no ranking officer would make, especially not twice. (00:03:10)
Suggested correction: And when was this established? If you are basing this error on modern American military protocols, there is no reason Starfleet in the 24th century would follow the same rules and traditions.
Yes, although it's not just American military introductions, it's pretty standard in most militaries to use full rank when making formal introductions, which has been followed for the most part by the writers, with other introductions that have happened onscreen.
Continuity mistake: In sickbay, when Nog walks over to Collins, he takes her hand and returns his gold Red Squad pin. In the closeup, Collins has a long, manicured thumbnail, but in the next shots facing Nog, Collins has short fingernails. (00:43:15)
Visible crew/equipment: After Joran supposes that he'll have to make himself more endearing, he suggests to Ezri that she visit the two victims' quarters to find answers. At the start of the next shot, the reflection of the boom operator holding up the boom pole is visible on the glass of the framed photo. (00:29:45)
Visible crew/equipment: At the start, during the briefing in the wardroom, everyone walks over to the table. And just as Sisko finishes saying, "The Seventh Fleet will be engaging the enemy in the morning," a white tape mark becomes visible on the floor at the actor's feet. (00:00:20)
In the Pale Moonlight - S6-E19
Visible crew/equipment: After Jadzia plays devil's advocate with Sisko, he tells her she would've made a decent Romulan. Then, when Sisko passes the camera as he walks around his desk, the blue T-mark is visible on the floor behind Jadzia. (00:06:10)