The bottom line is simple. They're not only ineffective, but allow the moles time to establish and become major problems. If you decide to use a trapper, insist on long term contracts. If you want to do the trapping, take some time to learn about a moles habits and biology. The mole's home range is measured in acres so almost any mole problem is usually a part of a larger mole population.
Trapping is a war of attrition.
It's labor intensive, time consuming, and it's effective. I have been trying to list moletrappers who provide moletrapping as a service in other cities and states. Although they are paid listings to defray costs associated with maintaining this site, I know some of them personally. Others I have talked with to get a good idea of how they provide their service before listing them. I have never been comfortable with per-mole trapping.