I've noticed that even with its relatively small number of users, it still takes a significant amount of time for a brand new installation of bitcoin to download all the transactions and be able to take part in the system. My Macbook Pro, for example, ran for many hours after installation before it had confirmed that a friend of mine had sent me some money.
So, my question is, what happens when orders of magnitude more users are using bitcoin? Will it take days, months or years to download all the transactions just to be able to participate in the system?
Does the system scale to the level currently supported by the world's existing financial infrastructure? From what I've seen so far, I doubt it. For example, could it support the volume of the New York stock exchange, which currently experiences volumes in trillions of transactions per day?