A B757-200 flight crew ignored a variety of red flags and nearly took off with the wrong airplane.

Narrative

This was a classic 'mental model' problem including a perfect setup; several discounted indicators that something was amiss; and Dispatch coming to the rescue in the end. We were scheduled and had paperwork to fly flight [123] but ended up pre-flighting; starting and taxiing the aircraft for flight [456]. We were the only crew at the office and we walked out to the only aircraft on the ramp; a B757. It was the same B757 we had flown in earlier that morning. Because of this; my mental model that this was 'of course' our aircraft was so obvious and so solid that all subsequent indications that something was amiss were discounted as an ACARS problem rather than the outrageous situation that we were in the wrong aircraft.[Several apparently aberrant ACARS and FMC anomalies found during preflight were ignored and manually corrected to conform to our certainty of being on the right airplane for the right flight.] Following the preflight; we started and taxied uneventfully. While holding in position on the runway for takeoff; Dispatch sent us a message advising he was confused about our aircraft and flight number. This was the first time it occurred to me that we might be in the wrong aircraft and I asked the First Officer to get us clearance off the runway until we could get it straightened out.We called Flight Control; confirmed the mix-up; and eventually worked out all the items required to make us a legal flight. Our flight was then uneventful. Earlier as I was performing the external inspection; I had noticed another B757 taxi in but paid no real attention. It turned out that we were supposed to be taking that aircraft and that crew would be taking ours.This last message from Dispatch was the key that broke my faulty mental model and allowed the many puzzle pieces to come together correctly. Careful; exact compliance with established procedures would have; of course; been sufficient to stop this chain of events.