Haha sorry- I didn't mean to turn this into another thread of this type. I do understand the security concerns, and I don't know of a way this could be technically implemented. Thanks for the detailed responses, though. I'm a newbie, and theres a lot of think about here.
My point really was just that, if a large portion of the world's scientific research (or something else equally important) were carried out on the quasi super computer that is the bitcoin network, bitcoin would have few enemies.
Offhand, the only thing I can think of is the following (and it is highly dependent on details that I don't know, but others might): Let's say that there is some unrelated application that needs to make a lot of hashes during its ordinary operation. Whenever it needs to do a hash, it takes the data that it is going to hash, uses it as a nonce for an unconfirmed bitcoin block, and then hashes the bitcoin block. If the nonce comes at the very beginning, then given most hashing functions, you should be able to grab the hash value out of the algorithm after just the nonce portion has been hashed, send that back to the application, and continue with the hashing until the full bitcoin block has been hashed. Then compare the final hash to see if it passes the difficulty or not. If so, you've confirmed a block. Either way, you've hashed your unrelated data.
Againey, I do find your idea interesting. I have no idea if the bitcoin infrastructure could ever be modified to this extent even if this were deemed to be a practical way of doing things.
My instinct- and this is still vaque, so pardon me if this is totally unreasonable- would be to keep the difficulty at a fixed level that the community considers totally secure, and require GPUs to perform an increasing ratio of calculations for some outside application (be it figuring out how proteins fold or looking for earth-like planets) to each random block generated. Thus, as more and more people mine, each miner carries out more calculations for the application and does less mining, but the mining difficulty hasn't changed.