Other mistake: At the end of the episode after delivering his complex greeting to the Jarada, Picard and Riker head for the Turbo lift. Just as they are about to enter, Picard opens his mouth really wide as if making a funny face to someone inside the turbolift or maybe quietly celebrating a 'successful take' given the bizarre nature of the greeting! Although it was filmed from the side it is quite easy to spot.
Continuity mistake: In the episode 'Yesterday's Enterprise' (season three, episode 15), watch the final scene with Geordi and Guinan in Ten-Forward. Although time and the universe has returned to normal, Geordi is still wearing the uniform from the alternate timeline (note the sleeve detail, and the extended neck piece).
Revealing mistake: In the scene where Barcley reappears on the transporter with the crewmember, they both fall to the ground. The transporter chief had put up a forcefield around the transporter chamber, in case something goes wrong. However, when the crewmember falls to the ground, his foot goes right through where the forcefield is meant to be. It is still active, as only a few seconds later we see it being deactivated.
Visible crew/equipment: Near the start, just as Riker says "You have all the time you need.", the engine consultant stops and turns around. As he does so, look above his head and you can see a microphone hanging down. The camera quickly adjusts so it's not visible any more. [Not visible in the remastered Blu-ray version].
Continuity mistake: In the scene right before the shuttle's crew finds the Romulan ship and the Enterprise, Geordi calls the shuttle craft's cockpit to explain the temporal disturbances. Captain Picard, Troi and Data walk into the shuttle's cockpit room and Troi puts her right arm on Geordi's chair. As Geordi, Data and Captain Picard are talking you can see Troi's wrist hanging off the chair, but when the camera cuts directly in front of Geordi her whole wrist is on the chair. The camera then cuts back and you can see that Troi's wrist is still hanging off the chair.
Plot hole: Apparently when it came to taking the ship into the asteroid, the entire bridge crew conveniently forgot that Galaxy class federation starships can separate. The obviously prudent course of action would be to separate the ship and send the star drive section (the narrower section) into the asteroid while the saucer section (the wider section) stood guard outside. The only reason this wasn't done was to provide drama for the rest of the episode when the Romulans collapsed the entrance to the chasm.
Other mistake: When Q the Judge enters on his throne, at one point, the hydraulic arm the throne is on is visible, despite being black to blend in. Conversely, in "All Good Things...", the final episode, the arm is missing having been matted out by CGI techniques.
Factual error: Shelby announces the Borg have entered Sector 001, and we get an exterior shot of the Borg ship flying past Saturn. The problem is that the Borg are approaching from the side of the planet illuminated by the sun, meaning they would actually be moving AWAY from Earth rather than toward it.
Continuity mistake: When Data and Troi are scanning the list of elements, searching for something to cause an explosion, the list is scrolling "up" the screen. When she tells Data to stop and go back, he does, but the list continues to scroll "up" instead of back "down".
Continuity mistake: In the scene where Data is brushing Timothy's hair into a copy of his own hairstyle, he stops, kneels down and asks Timothy "Timothy, are you having bad dreams?" In this shot there is a big tuft of hair on the right side of Timothy's head that sticks straight out. When their conversation is over and Data stands up in the wider shot, all of Timothy's hair is in place.
Visible crew/equipment: In the opening scene when Data is portraying a character from Shakespeare's play "The Tempest" a small card can be seen attached to the back of the book he is carrying (likely containing his lines), but after increasing the amount of torch light the card is no longer there.