How does this scale?

If the Bitcoin network ever reaches a level even close to that of Visa, then there will be numerable finacial institutions with a clear, vested interest in the security of the system; who are very likely to run dedicated servers (if not entire server farms) to keep the system secure and competing institutions honest. It will still be possible for an individual to dedicate his own resources to set up such a server, but most users will not need to participate.