Re: Alternative history: the invasion of Constantinople
Well, at least two consequences seem fairly clear to me. A victory in the Dardanelles and the successful invasion of Constantinople would have allowed a much easier supply route between Russia and her English and French allies. They still would have had to fight to protect that route, and the German naval forces were a force to be reckoned with, but some difference would have been expected. That's one. Two is, that possession of Constantinople would have opened up avenues of approach from the South, extending the number of fronts the German's would have to cover. That works both ways to some extent -- the allies would also have to consider that extra front, but from an offensive rather than defensive position.
The wild card, as I see it, is not the strategic value of these gains, but what Germany and her allies would have done in response. Ingenuity is impossible to guess, and it's possible that they'd have come up with a response different from any we could imagine.
But assuming that the British managed to hold on to Constantinople throughout the war, and the allies still won (which seems reasonable, but you never know how a premature victory will effect the long term goal), I would imagine that they'd present a fairly strong case at war's end for Constantinople remaining in British hands. There, I think, is where the real historical changes would start, because a British occupied Constantinople would have had huge effects on the subsequent development of the region. The formation of the Baltic states, for example, would likely be radically altered.
Anyway, there's one potential starting point for considering the question.