Continuity mistake: When David and Saavik approach Spock's tube on Genesis, you can see quite a bit of dirt covering the words' red lettering, but when it does another shot of the lettering, it is noticeably cleaner. (00:30:25)
Continuity mistake: In the scene early in the movie where Kirk is talking to Sarek the guns on the wall are suddenly rearranged. (00:23:50 - 00:24:45)
Revealing mistake: When the Enterprise explodes, some of the debris briefly turns transparent. (01:12:15)
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.
Trivia: At the beginning of the movie Kirk rescues McCoy from a jail of some sort. Before leaving Kirk asks McCoy how many fingers he's holding up and does the Vulcan hand thing. However, Shatner had severe difficulties putting his fingers into place, they just wouldn't hold into position. So the crew wound up wrapping fishing line around Shatner's fingers, he would put them into position out of the camera and the shot quickly jumped while his fingers where still in place. If you look closely you see the line around his fingers. (Note that this problem occurred several times during Star Trek, actually, Nimoy and Leonard seem to be the only people doing this without a problem.)
Question: When Commander Morrow responds to Kirk's protests he says "Jim, the Enterprise is twenty years old. We feel her day's over." In ST: TMP, Decker said "This is an almost totally new Enterprise." If the Enterprise was, for all intents and purposes, totally rebuilt from the original, with more space, better engines, etc., how could it be twenty years old?
Chosen answer: The Enterprise may have been extensively refurbished, but that does not mean it is entirely new. The ship is still 20 years old. Also, that was Decker's comment, and it may have been an over-exaggeration. Newer ships were being designed and built in the meantime, so even if the Enterprise was still mechanically sound, the technology may have advanced so much that it was not possible or it wasn't economically feasible to continually retrofit older vessels.
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