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.
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?"
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.
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.
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.
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)
The Way of the Warrior (1) - S4-E1
Visible crew/equipment: At the start, after the Changeling surprise drill's staff is dismissed, while Sisko and Nerys are walking away, when she asks, "How about some dinner?" at the bottom left side of the screen, there are multiple T-marks visible on the floor behind her, ending with a pink T-mark as Sisko exits. (00:02:30)
Visible crew/equipment: After Odo orders two glasses of champagne for Dr. Mora and himself, when it cuts to the birthing ceremony as Y'Pora walks towards Nerys, there are three T-marks (one blue and two green) taped to the floor, at the bottom right corner of the screen. (00:33:10)
Visible crew/equipment: When Jadzia walks into Kor's quarters and finds Kor on the floor, just as she helps Kor stand up, there's a visible T-mark taped to the floor beside the chair. (00:08:35)
Resurrection - S6-E8
Visible crew/equipment: When Bareil enters his quarters and finds Intendant Kira dressed like Major Kira, just as Intendant Kira walks towards Bareil, in the mirror we can see the reflection of a crew member wearing a white shirt and shorts. (00:36:55)
Visible crew/equipment: During the last scene in the infirmary, Bashir has a word with O'Brien about Garak's condition. Then, just as O'Brien walks towards Garak, on the console's reflective surface, we can see the reflection of the moving boom mic (beside the ceiling's black stripe pattern) at the bottom of the screen. (00:42:50)
Visible crew/equipment: After Kai Winn grasps Sisko's ear to feel his pagh, it soon cuts to Jake delivering half the items to Dr. Giger, and when Giger removes the chip that Jake brought on the cart, the actor's yellow tape mark is visible on the floor near Giger's consoles. (00:31:00)