Again this morning I've been sat on the throne, as is my want, where I do all of my philosophising and my best ideas originate :O)
How about a one off payment for each puppy when born, this can be re-couped by the breeder when selling, and this payment covers vets fees for taking the dogs DNA. The DNA is then kept on a central register.
When a dog dumps in a public place the warden can then get a sample and the dog can be traced. A hefty fine can then be made, large enough to help with the salaries of the wardens instead of ALL rate payers, including those who don't own a dog, having to pay for wardens.
Hereford has certainly cleaned up it's act for a long time now, certainly in the areas I frequent, but there are still the odd dog owning moron out there who sticks his/her fingers up to society. I'm sure these are also the late night dog walkers that go out after dark. Only this morning while driving down the avenue where my daughter lives there were two separate dumps, same colour and size so probably the same dog (I didn't test the consistency). It wasn't there yesterday evening when we called at my daughters.
As the owner of three dogs I'd be willing to pay as long as it stopped the mess and the anti-social lowlives from owning dogs.
How you stop cat mess is another matter (forgive the pun).
I'm afraid my philosophies about curing the problem wouldn't be received by cat owners very well ... heh! heh!