The big piece of evidence point to the Earth-to-Vulcan travel time being unreasonably short is Sulu telling Pike they've reached maximum warp, which starts an unbroken stretch of action that goes all the way to the Enterprise arriving at Vulcan. There is a time gap just before that, when Kirk passes out, which lasts at least long enough for McCoy to change uniforms. Kirk could be unconscious for seconds, or he could be out for days, but the kicker is that they ship probably should hit top speed earlier than the last couple minutes of its journey unless the entire journey only lasted a few minutes. It's hand-waveable, but awkward.
Well, Kirk being unconscious for a short while is fairly unlikely as a thing; would McCoy really have calculated the dose that way? But yeah, Sulu's comment is the problematic bit here. And no, Chekov's last-minute PA to the crew is not: Kirk did that all the time, if he even bothered to inform his crew about upcoming or current events at all.
Then again, Sulu doesn't say anything about reaching, merely that they
are currently at maximum warp. Perhaps he's obligated to say that every thirty minutes or something, there being no Scotty there to whine about 'em poor bairns?
No, the really hard one to figure out is STID, where the trip from Earth to the edge of the Klingon home system takes an ambiguous amount of time, but the trip back seems to cover only a couple minutes, unless, again, McCoy waits several hours for no reason before checking out Khan and telling him they've fled the Admiral's ship. ,
...And to say "at least we are moving again", as if that were news to
him. That is, he seems to be muttering to himself in order to reassure himself; Khan just overhears.
But Scotty also quips that all the action, to Qo'noS and back, has taken place within one day. So the trip out can't have been all that slow, either. Not mere minutes long, though, not necessarily. And it's certainly a case of careful-and-stealthy out, all-stops-out-emergency back in.
Worse than that is that is the dreadnaught knocks them out of warp inside the orbit of the moon; one, the Enterprise really should've already slowed down if they were that close
...Why? Marcus could park with precision when he warped to Kirk's comfort zone in Klingon space. If Sulu chose to brake "early", it could have been 201 km off Earth rather than 200.
The problem here is that the ship seems not to be under Sulu's control when emerging, but spinning madly - yet she emerges from warp in the Sol system, rather than fifteen lightyears outside it. Why and how did Marcus force Sulu out of warp that close to the destination?
two, the Admiral has already failed in keeping Kirk from getting to Earth and telling Starfleet about his dastardly plan; even if communications are jammed, they can still just look out the window and watch Admiral Robocop murder their golden-boy with a mysterious, evil-looking starship.
And then cheer for their champion who saved Earth from that juvenile terrorist.
How mysterious is that ship, really? Marcus had a desktop model of her in his office. Probably those are being churned out in sufficient numbers already for Marcus to launch his war, and Kirk just happens to be one of those who don't need to know. Doesn't mean Marcus would get into trouble for not telling.
Beyond is a bit better, if only because nobody does anything while the ships cross through the nebula aside from crossing through the nebula, so it's easy to imagine it takes as much time as seems reasonable to cross the nebula.
...Such as fifty million years? The ship moves very literally at a walking pace when we watch her brave the rubble (I could certainly outrun her on a good day) - and it's rubble all the way from Yorktown to Altamid! Or at least we see the same superdense rubble right next to both Yorktown and Altamid.
Basically, we're forced to think that Yorktown is deep in the Altamid system, and indeed has been built there for the specific purpose of exploring the nebula, once navigation systems make it safe for things other than automated probes (and Krall no doubt made it look worse than it was, by sending false signals back via the Magellan channels). The nebula surrounding the iner system then is much less than an AU thick, and has its densest parts at the edges or something.
That Kirk could do even half a minute of warping inside the "nebula" seems out of the question.
Timo Saloniemi