I have to wonder how it would take Spock so long to spot a simple number transposition. This is a guy who calculates things to multiple decimals off the top of his head.
Remember, though, how it happened. The first coordinates, the ones to the fake ship, were received by Spock via Uhura, on the Bridge. But the second set, to the Council chambers, were received by Scotty in the Transporter Room. We don't know if Spock ever overheard those being given; he was up at the Bridge at the time.
In the scenario that makes sense, Spock did
not overhear anything, but eventually formulated a hypothesis and asked for the two sets of coordinates from the two separate people involved, thereby confirming his hypothesis.
Yet does the transposition trick make sense from the Gideon point of view? They first stun Kirk, then unleash him in the fake ship; they could just as easily allow him to beam down to the Council chambers first. And they seem to have their own transporter, from which Kirk emerges in the teaser, after the stunning and sampling is already done. Why risk using two separate beam-down sites, then?
The whole point of the trick is to play time against the likely
Enterprise response where an armed landing party beams down to the coordinates where they think their Captain went, then secures that site and starts to spread out. If they beam down at the wrong coordinates first, it takes them longer to find Kirk and disrupt the operation - the longer, the more distance there is between the two coordinates. But providing the heroes with the correct set in addition to the fake set gives 50% odds of the raiding party hitting their target immediately and dead center...
Ultimately, though, the Gideonites need not worry. Their blood sample has already been taken; Kirk is supposedly only being held as an insurance against something going wrong, and nothing does appear to be going wrong. Let the heroes raid the place - it's too late for them to do any real damage there. So the trickery need not really be elaborate or watertight or anything. At worst, the UFP might decide to nuke the place in anger, a very welcome turn of events where the population would be slightly reduced even before the disease shortens lifespans!
Timo Saloniemi