On top of that, they entered the turbo lift shaft from an access door on the bottom deck and flew all the way up to the top of the shaft. Where was the turbolift?
The turbolifts not only move up and dowm but also move side to side. It is possible for a up/down shaft not to have a lift pod in it. With a ship that big you need to be able to get around by some other means than walking.
Ok, lets be REALLY picky. In every Star Trek episode I have ever seen, every star trek book, manual, etc. etc. etc., the Bridge at the top of the ship is deck one and the decks are numbered down from there. So if they are going up, why are the deck numbers also going up? The deck numbers should be decreasing as they ascend.
In a special I saw on Sci-Fi (hosted by Leonard Nimoy) this c*ck-up was attributed to the director who wanted to give the audience a dramatic effect of, "Oh my god! Look how high up they're going!"
Also if you look closely Kirk and McCoy aren't holding on to Spock as they are going up the turboshaft. They were just leaning on him. They would have fallen of of Spock as they were going up. So that makes four mistakes in that scene.
Same scene another mistake: When Kirk and McCoy join Spock they each step onto one of his anti-grav boots. However in the next scene when the audience is looking down from their perspective, Kirk and McCoy's feet are shown dangling next to Spock's Boots....OOOOps!
To draw even more attention to this mistake, just as they reach the top, Kirk and McCoy throw their hands upward. Thus, their arms are up while their feet are dangling! It's unbelievable that the film editors missed something so noticeable.
It is also important to note that there is not a central turbolift shaft which would run continuously up through all the decks of the ship. The only conceivable location which would allow them to shoot up perhaps 12-15 decks would be from the bottom of the secondary hull, up through the connecting dorsal to the primary hull.
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