A miner on one of the other consortia asked me what I thought of a proposed 'karmacoin' in which instead of hashing to authenticate transactions, your miner program was doing something more genuinely useful.  I replied that
i) I thought it a bad idea to make up more YetAnotherBitcoinClones
ii) I liked the karma idea and proposed that for public benefit tasks such as following asteroid paths or ridding the world of malaria, perhaps stratum and bitcoin mining consortia would have the right infrastructure to share out a problem amongst thousands, and distribute payment for subroutine completions (not hashes, since most tasks are not hashing).  That would need a generous benefactor to put 1000 BTC on a problem from time to time, and it would need some transparency so that the public can see that they are not computing the most economical way to smash an asteroid into the pentagon.  That would gain the benefactor massively parallel processing power so might be suitable for certain classes of task which suit that degree of parallelism.

What do others think?
Would it be better to install new code to do karma tasks for bitcoin than to have a new karmacoin?
Would you want to connect in to processing tasks at an existing bitcoin mining consortium?
Should effort shares be counted and rewarded in Bitcoin, or would people not need those to help out with a problem?