Factual error: While the Leonov has a centrifugal section to simulate gravity, the ship's bridge is not part of it (evidenced by the stationary views outside its portholes). Yet in various scenes, including the one when Floyd rushes in to discuss his plan to return to Earth sooner with Tanya, gravity seems quite evident. Floyd marches across the compartment onto the raised pilot area's floor, then steps down from it, his foot landing audibly. Tanya's open jacket also hangs down normally as she moves about. Yet when Floyd demonstrates his plan using two pens, they float in mid air. (01:26:50)
Factual error: Right after Kyle saws off the barrel of the shotgun in the alley, he pumps a shell into it, then again after his dream of the future in the car, then a 3rd time in the night club before he shoots the terminator. The 2nd and 3rd time he pumps it, shells should eject. They don't. (00:35:22)
Factual error: According to "The Doomsday Machine", full impulse drive is one-quarter the speed of light. In the first two movies, Enterprise used thrusters as opposed to impulse drive to leave Spacedock, confirming the notion that impulse drive is far too fast to leave such a (comparatively) small structure. Styles, however, orders Excelsior to one-quarter impulse, which is 18,750 km/s. In one second, she will travel half again Earth's diameter. From the time he gives the order to the time we see Excelsior clear spacedock's doors is approximately 40 seconds. Even allowing 30 seconds to go from rest to one quarter impulse, spacedock must be 13-15 times bigger than Earth! That's some serious engineering. (00:23:45)
Suggested correction: I reckon the writers always refer to levels of "impulse power" precisely so they don't have to worry too much about particular speeds (personally I always thought of it as roughly analogous to gears on a vehicle, but your mileage may vary). They use impulse to leave dock in both Star Trek II: The Wrath of Khan and Star Trek VI: The Undiscovered Country (it's implied to be unusual in both cases, for what it's worth). If all of that contradicts an earlier episode, I think we're looking at more of a retcon situation than a mistake.
Suggested correction: The warp scale has been adjusted several times, so it is impossible to say precisely how fast this fictional technology is, and by extension, how fast impulse is.
Impulse drive speed on starships have been consistent. Although sometimes quarter impulse on a shuttle refers to quarter power and not speed. Even if the speed of quarter impulse is 10 times slower than suggested (and used in the series), spacedock would still be 1.3-1.5 times bigger than Earth, which it wasn't. "It's fictional technology" is usually only a valid correction if the technology isn't explained in-universe. However, when certain parameters regarding fictional technology are established (even if they set wide parameters such as warp speed velocities) violations or contradictions (through bad script writing or whatnot) are valid mistakes.
Factual error: When Glen and Nancy are talking on the bridge, you can see huge palm trees in the background. Though this was filmed in California (hence visible palm trees at the cemetery), the fictional Springwood is supposed to be in Ohio - they show the location of Springwood on a map at the start of 'Freddy's Dead, the Final Nightmare', and there's no other conflicting in-universe location given within the series. So it's established as Ohio, but there are no palm trees in Ohio. Other California "hints" add to the mistake, such as CA license plates, etc. (00:01:00 - 00:43:22)
Factual error: When Axel and Taggart are taken under fire by the gunner with the dark glasses (who is shot by Billy), notice that the gunner stands perpendicular (i.e. at a 90° angle) to the stairs where Axel and Taggart take cover. Yet, two of the bullet holes appear in a column at the base of the stairs which would have come from a different trajectory, namely in line with the stairway and thus from Axel and Taggart's flank.
Factual error: Thompson wears moderately high heels in uniform and undercover. Unless she was working strictly in the office, she'd be required to wear tennis shoes or at least flats so she can run.
Factual error: In the scene with Tempest (the video game in the cinema's foyer), Regina is annoyed to find the tag 'DMK' shown in the scoreboard, which she otherwise dominates, and she sets out to remove it. After completing a game which scores higher than 'DMK', she overwrites his name on the scoreboard and her name is both above and below. If this had been a real video game, his score wouldn't have been removed from the list, it would have just dropped down one place. She would have needed to play several games, bettering the 'DMK' score every time in order to own the board again. She would just keep knocking DMK down the list, she could only overwrite the last place.
Factual error: When Andy and Charlie have caught a cab (allegedly in Manhattan), and the agents are running after the car, we see green letters reading "Manor", which is a movie theater in Wilmington, NC. (00:03:19 - 03:26:00)