When Beverly strokes Dr. Manheim's hair and says she wished she could talk to him, she is stroking his hair with her left hand while holding 2 instruments in her right. When the camera angle changes, she is suddenly holding 1 instrument in each hand.
In the holodeck café, when Francine says to Gabrielle that they have waited long enough, she sits with her legs parallel to each other (visible when you look very closely). Yet in the very next shot, as Gabrielle replies to her, Francine's legs are crossed.
While Picard is talking to holographic maître d', he has his arms straight down on a ledge. When the camera angle changes, Picard's arms are suddenly folded in front of his chest.
The automated distress call coming from the station toward the beginning of the episode only gives two coordinates for the station's location. In three-dimensional space, three coordinates must be given.
When Data puts the antimatter in the stream, he asks for a 27 second count down. Data has an internal chronometer and is notorious for giving arrival times down to the second. He is also capable of handling multiple calculations and thoughts at the same time without distraction. Why would he need an external audio countdown? Data requested the external audio countdown before the time distortion occurred because he knew that, when it occurred, there would be more than one of him and then could link his chronometer with the correct dimension.
On the Holodeck, Picard sees the Eiffel Tower directly in front of him. In another shot, while talking to the server, it is seen behind him.
However, as he is on the Holodeck, the computer program can easily present different views of Paris.
Jenice tells Picard she waited at the café all day for him, and that it was raining. The fact that the café recreated by Picard on the holodeck is an open-air café does not guarantee that the original café didn't have indoor seating facilities as well, nor that Jenice waited outside all day in the rain. Her 'it was raining and you couldn't find a cab' line was made while riffing on his excuses for not showing up, which would not reliably indicate that it was raining on that day (especially since the holodeck would know whether or not it was raining on any date specified and provide it, which it doesn't); however, she next states in all seriousness that it rained that day as well as through the following week - which still doesn't prohibit Picard from changing his program to a fair-weather day for an ideal romantic setting.
When discussing the Blue Parrot Café, Picard tells Troi that she's buying. The Federation does not use money. However, this merely an expression similar to the American habit (admittedly dying out now) of saying to a guest, in own's own home, "Can I buy you a drink/coffee?"
In The Big Goodbye (1988), the entire bridge crew appears to have no idea what an automobile is and has to have Data explain it to them; however, when Mrs. Manheim lists some of the excuses Picard could have used, she says 'It was raining and you couldn't find a cab'. Picard immediately acknowledges this without hesitation or confusion. If he didn't know what an automobile was, it seems unlikely he would know what a cab was. However, a cab or taxi need not be an automobile, in the sense of a car with an internal combustion or electric engine. On Earth, in the 24th century, they presumably have cabs but they are probably driverless, automated vehicles.
In the professor's lab, Data jumps twice to avoid the automatic weapons fire from the security system. Both times you can tell it's a stunt double. The second time, he jumps behind some equipment. Watching the shadows, the double moves so that Data can come forward to return fire.
The conference room is on the same level as the bridge and facing backwards, yet the back section of the saucer, the warp nacelles and the far end of the engineering section do not appear in the window. This is seen throughout the series and is done simply to avoid the huge expense of multiple CG renderings and multiple camera angles for everything filmed on that set. Some forty years later, this would present far less of a problem but at the time there was no other practical alternative. As is, the blue screen visuals are of stars passing from one of three angles, depending on the shot.
Picard programs the holodeck recreation of the café for a specific date and time. Unless the Federation employs extremely invasive monitoring of every square inch of its space at all times, and makes that data widely available to Starfleet service members, it is extremely unlikely that such a request could be fulfilled.
When Data beams down alone, the shadow of a boom mic can be seen behind and above him.
Whilst receiving co-ordinates to their destination, Worf pronounces longitude as longtitude.
In the final scene in the holodeck, when Jenice tells Picard that she'll always expect him to come charging to her rescue, he responds "I'll do my breast," rather than, "I'll do my best." This is either a flubbed take that made it into the show or a Freudian slip on Picard's part.
When the Manheims are beamed to sickbay, Picard takes Riker and Data, the two next-highest ranking officers on the ship, with him to sickbay and neglects to hand command over to anyone else.
When Data puts the antimatter in the stream, there are three of him. A brief discussion of which one is in the correct timeline has him saying "It's me". 'It's' is a contraction and Data does not use contractions.
Two of many incidents which contradict the notion that Data cannot use contractions: first, when being asked to go to the lab, he replies "Times flies when you're having fun," and second, when he drops the anti-matter in the time rift, saying, "It's me!" (Data also uses what was once deemed to be bad grammar. According to pedants, the line should read, "It is I!" but, even now, it is regarded as overly formal and "It is me" is accepted.)