Indeed, we can handle that bit properly out here.
Beaming within the ship is not a problem in the 2250s. It wasn't much of a problem in the 2150s, either (cf. the ploy where Archer is "executed" by the transporter"). And it is not a problem in the 2360s or 2370s. It only ever was a problem in a ship careening out of control at high warp at a time an alien was turning people to violent idiots...
Yet beaming folks
out of a stuck turbolift is
always a problem. We get turbolift tension in DS9 twice ("The Forsaken", "Crossfire") and in TNG once ("Disaster"), plus these times in DSC, and beaming out is never an option.
Might be turboshafts are handy spaces for putting the high cochranage plasma conduits in. Might be turbocabs are shielded since they double as lifepods (see ST:B). Might be Number One and the Chief Engineer have a good thing going with this "Ooh, the lift got stuck again!" trick - the XO isn't really busy dictating a report on that PADD, but carries it solely for signaling the Chief that the Ensign indeed is a looker (thanks, Yistaan).
Generally, I'd think the transporter would have no problems with accuracy anywhere: most targets require millimeter precision. But a starship would be a more demanding target than the average planetside palace or cave or jungle, with a much higher density of things that can fry you when you're a helpless blob of phased matter. So, you pick and choose your intraship transports, and generally you avoid them. But not when you are from the Mirror Universe and portraying a daredevil on this side, too!
Timo Saloniemi