Not sure that dampness per se is reason enough to report a landlord to the authorities, but I have seen it become grounds for breaking a lease when the dampness was so great that it caused mold to grow on the walls of the place and on the tenants belongings- fortunately for everyone involved it was harmless mold- but it did render the dwelling uninhabitable so the tenant got out of the lease with no penalty. In the states, this would fall into one of those legal gray zones where it isn't really clearly defined who has what rights under the law. I think dampness alone wouln't be grounds for any action, but if the dampness was negatively affecting the integrity of the structure or denying the tenant "quiet enjoyment" of the place or rendering the place ininhabitable (according to health and safety regs..), then there might be something concrete to report, but a "cold drafty old place" in and of itself wouldn't really be anything that would get anyone's attention down at city hall. "Caveat Emptor" is the guiding principle for renters over here. Unfortunately this also creates a nurturing environment and economic incentive for slummy landlords as well... Maybe an answer would be to have biennial health & safety inspections; but landlords would never go for this..