As mining works now, miners have to verify all Bitcoin transactions in the blocks they mine, because they would otherwise risk producing an invalid block. This is problematic because many miners are Chinese, and thus have poor Internet connectivity, so it would be preferable to separate the task of creating valid proof-of-work from the task of collecting valid transactions.
This could be made possible by adding an opcode that checks whether the top-most stack item is a valid block header, we could call it OP_VALID_HEADER(VERIFY), thus allowing miners to be paid for a valid block header through a regular Bitcoin transaction, rather than through the coinbase transaction only. This allows a different group to simply act as collectors of transactions, and create OP_VALID_HEADER-transactions that pay to block headers with a merkle root that includes all the highest-fee transactions.
So, these collectors would accumulate as many connections as possible within the Bitcoin P2P network, and collect all the highest fee transactions they can find. Then construct a block which includes all these transactions, and a coinbase tx that pays the block reward plus fees to the collector.
With this block the collector would then create a Bitcoin transaction, with a OP_VALID_HEADER-output that can be redeemed by supplying the block header in the script but with a modified nonce/timestamp such that the proof-of-work+timestamp is valid. Miners would then only have to look for these Bitcoin transactions from the collectors, and mine on whichever header pays them the most, without having to care about whether the block in question includes invalid transactions, because the miner is paid for just a valid proof-of-work hash. When the miner finds a solution, it publishes the transaction, the collector see this transaction, gets it valid header, and publishes the block.
A side bonus of this is that botnet miners can now participate on basically equal footing with traditional miners: they just listen to the P2P network for the transaction from the collector who pays them the most, which will include as many transactions as possible to earn the most in fees, thus verifying transactions without having to do the work.
/Rune