I am wondering, how easy would it be to make a lightweight version of bitcoin-Qt. The difference being that it won't store the blockchain locally but instead query connected nodes instead for the needed information.
If it's able to establish enough connections, and connect to the network in the same way as a full-node, but behaving much in the same way as a node that's not yet downloaded the blockchain, and there was a small modification made to the protocol that allowed the necessary queries - perhaps an extension to the protocol rather than a change to it, and full-nodes can choose whether to opt-in to help provide this service or not.
I'm not very familiar with how other lightweight clients do it so far, to see how this idea compares. Also, people could configure their lightweight bitcoin-qt's to specify which full-nodes to consult, thereby allowing people to configure how much they can trust it. I see the main miners being good souces for such co-operating nodes, and already my full-node obtains most of it's blocks from one of the significant mining pools.