How about if the Hungarian canon maker who sold artillery to the Turks had been more interested in helping Christians than in making a profit, and the big guns had been pointing the other way?
Of course that could have played out for good — the city is saved, the next push by the Muslims, either the West or the Rus come to the aid of Constantinople in the ensuing war Islam is pushed back into Arabia or even eradicated — or for ill — the next siege, a generation and a half later, succeeds, and when the Turks push into Romania, Vlad the Impaler is long dead, they meet no effective resistance and overrun Europe.
That's what made me think about these scenario in the first place. If one piece of advanced technology (for that era) could make such a difference, imagine what one piece of "modern" technology (ie. an M-2 machine gun) held by the defenders of Constantinople from the top of their walls would have done to Mehmed's 80,000 soldiers below the walls.
I haven't ready my Byzantine History in a while, but I remember reading somewhere that Hungarian engineer actually hoped to sell his ideas to the defenders of Constantinople, but dismissed him as a crank (or couldn't afford to pay him) - will have to do some research on that.