[nhaehnle]

It depends on what you mean by verifying the transactions. Checking the signature of the transactions, to prove that the transaction was in fact issued by whoever owns the coins being sent, is only a negligible part of the computation.

The actual pointless task is to try to find a type of hash collision, to be specific: find a plaintext containing hashes of the transactions to be committed such that the hash of this plaintext starts with a bunch of zeroes. The more initial zeroes you require, the higher is the difficulty. (The plaintext is allowed to contain a small arbitrary nonce. So miners just cycle through all the possible nonces, computing hashes, until they find one that starts with a bunch of zeroes.)

It's conceivable that one could somehow mix the transaction data into a problem of bioinformatics, but I don't know so much about that. The problem is that, as far as I'm aware, some hash of the transactions to be committed must be part of the input of the "pointless" problem.