One of the nice little details in TWOK was when Kirk and Saavik carried on their conversation while disembodied in the transporter beam, when beaming up from the Genesis Cave. The idea that life continues uninterrupted during transport was of course taken to the next level in TNG: The Realm of Fear. The transporter not interrupting any biological process at all, including cognition and consciousness, could be one portion of a convincing argument that what comes out at the other end really is the original.
For me, that bit with Kirk and Saavik stretched my suspension of disbelief to the breaking point. How can two people communicate verbally when their vocal apparatus, their hearing apparatus, and their brains are dematerialized? It reminded me of the scene in The Fly
where Dandelo the cat fails to re-integrate, and yet somehow we hear his ghostly meows echoing in the ether.