Remembrance - S1-E1
Character mistake: Picard and Data are playing poker at the beginning of the episode. Before the actual faces of the players are revealed, we are shown close-ups of their hands as they put down the chips for the bet. When Picard says his first line in the series it's "See", and it is literally true, because in the previous shot, Data put his 5 cards down on the table and face up. (00:00:50)
Factual error: Picard tells his manservant that Laris and him are more needed at the Chateau than with him in space because there's less than a month left before the harvest. Without being privy to the knowledge of a XXIV century agronomist, grapes at the Chateau are grown with traditional methods in a climate that looks reasonably similar to our own. From the establishing shot at the beginning of this episode and what we could see by his walk in the vineyard in the previous, there are no grapes forming, ripening, not even flowers. Hardly the look of a vineyeard close to harvest. (00:07:00 - 00:36:10)
Continuity mistake: When Lieutenant Narissa Rizzo appears in holo form in the last scene of the episode, the two pins of her rank on her right breast initially are attached together (as if the two magnets have been placed too close together and ended up being pulled to one another). During the first part of the scene they go back and forth between being joined and separated. (00:40:45)
Remembrance - S1-E1
Continuity mistake: When Picard walks out of the archive building he's shocked to see Dahj, who is wearing boots with a chunky heel (also seen when she followed Laris to a bedroom for "a good night's sleep"). After their talk Dahj and Picard head to the roof, and while Dahj fights the Romulan assassins she is wearing flat soled boots, but in at least one shot as she kicks an assassin her chunky heeled boots reappear. (00:28:15 - 00:32:45)
Remembrance - S1-E1
Continuity mistake: Right at the beginning, the camera zooms into the Enterprise through a view that shows 3 windows of equal size. In the rest of the scene, Jean-Luc Picard and Data are playing poker in front of two side windows and a central window that is wider than the other two combined. (00:00:30)
Character mistake: Dr. Agnes Jurati, one of the Federation leading scientists, is bored during the hyperspace travel, and so she chats a bit with the captain. While she gives her quirky speech, she casually mentions that "there are over 3 billion stars in our galaxy." She's not wrong, technically, but the number of stars in our galaxy is estimated between 100 and 400 billion. She is way off. (00:08:40)
Suggested correction: Two things. You state that she's not wrong, which she isn't. The fact that she chose an odd turn of phrase doesn't make it a mistake. Plus, you reference the number of 'galaxies' in our galaxy but I am guessing this is just a typo.
The End Is the Beginning - S1-E3
Continuity mistake: When Commodore Oh appears in an odd Men In Black cosplay to Dr. Agnes Jurati in Okinawa, Agnes removes her earplugs and lowers her arms, but in the next shot she is still shown with her right hand raised. (00:16:15)
Plot hole: Some part of the dialogue between Jean-Luc Picard and Admiral Kirsten Clancy must have been left on the editing room floor, because when Commodore Oh refers to the conversation the two had, says that "He referred to Zhat Vash by name." He did not. (00:21:30 - 00:37:30)
Remembrance - S1-E1
Other mistake: Picard gives the mysterious girl some Earl Grey. She has it in hand only in one shot, the faraway one when the two Romulan servants are leaving. The way the scene goes, at no point during the whole scene does she have time to even take a sip. (00:19:05)
The End Is the Beginning - S1-E3
Continuity mistake: At Raffi's home, when she rips into Picard and tells him how she had lost her security clearance and more, Raffi stands up and grabs both the bottle and red glass then walks away from the table. In the overhead long shot, as Raffi walks down the steps the bottle is in her right hand, and her left hand is empty, then when Picard stands up we see Raffi's red glass is back on the table near her chair. (00:10:30)
The End Is the Beginning - S1-E3
Continuity mistake: When Raffi figures out Maddox's location through her drunken handwaving, she is holding the jar by the neck at different heights between shots. (00:22:20)
The End Is the Beginning - S1-E3
Continuity mistake: Picard, panting after the walk through Vasquez Rocks, tells Raffi he's sorry. Michelle Hurd in the first close-up and wide shot has her hand on her knee, with the arm coming up from the inside leg. In the close-up that follows, she is leaning her face on her hand as it comes up from the other side of the leg. From then on her head position changes inconsistently as well. (00:14:05)
Remembrance - S1-E1
Continuity mistake: Dahj shows up in the middle of Picard's vineyard. In the shot when she asks "Do you know me?" the shadows behind her differ greatly from the rest of the scene, where trellises cast hardly any. (00:17:20)
Remembrance - S1-E1
Continuity mistake: Dahj kills the 3 dudes who tried to subdue her putting a bag on her head. When the third one kicks the bucket, notice how he falls with his leg spread, a tablet-like object rolls on the floor touching the carpet, and on the carpet itself there are several pieces of debris and shattered glass. In a following shot the bag that was totally not hiding a stuntwoman doing agile flips and kicks is removed from her head and we see Isa Briones standing barefoot. She stands on that same carpet but it has been sanitized from anything sharp, while the aforementioned Romulan lies on the floor positioned differently and the 'tablet' is gone. (00:06:00)
The End Is the Beginning - S1-E3
Continuity mistake: Picard during his conversation with Raffi on the bench outside the Federation HQ building is at one point sitting with his arm folded, no tablet in hand or lap. By the end of the convo, without him moving, the tablet reappears in his arms, clutched to his chest. (00:04:55)
The End Is the Beginning - S1-E3
Continuity mistake: After plucking some of her space opium (snakeleaf), Raffi tells Picard "You've got some goddamn nerve", and drops her hands. But in the reverse shot, her hands are back up at waist level. (00:08:35)
The End Is the Beginning - S1-E3
Continuity mistake: In the last phase of her conversation with Picard, when she sends him away, Raffi changes position between shots, so her pigtail is on/off her knee. (00:15:30)
The End Is the Beginning - S1-E3
Continuity mistake: Zhaban put in a bag some delicacies for Picard. When he mentions "Madame Arnaud's terrine d'oie" his hand is holding the jar in the first shot, during which you can see his hand turn to hold one of the bag's handles. But in the reverse shot he is still holding the jar, and puts it in the bag. (00:27:10)
Remembrance - S1-E1
Continuity mistake: Just as the Romulan assassins transport into Dahj's apartment, her boots are lying on the floor beside the table right before they murder Dahj's Xahean boyfriend, but when they walk over to Dahj and slam her head onto the table, her boots are now standing properly upright side-by-side. Additionally, when the assassins place the hood over Dahj's head and she tosses one of them behind the sofa, the three pillar candles to the left have no flames whatsoever, but then all three flames return. (00:05:10)
Continuity mistake: At the reclamation site Soji whispers to the Borg drone, "You are free now, my friend," and then it cuts to Chateau Picard. When Picard opens the desk drawer, in the wide shot he removes the silver box with his left hand and is about to place it atop the desk, but in the next closeup the box is now in Picard's right hand as he sets it down. (00:32:25)
