As an energy-efficiency measure my experience is that, after making sure doors and windows are draught-proof, this is the single most cost-effective energy-saving measure there is. When we had it installed in our house we noticed immediately that the main rooms held on to their temperatures overnight once the heating had been switched off. (Obviously this is only relevant in winter!) Our annual gas bill was substantially more than the (heavily-subsidised) cost of installation, so I reckon this returned our investment within a couple of winters.
Since water vapour doesn't naturally seep through walls or windows there are only two places where it can potentially cause damp problems: if it occludes the small amount of draught under the roof eaves which keeps your loft dry or if it blocks the under-floor vents (the airbricks that you see at the base of your house). The firm that installed ours checked both and changed two air bricks. On the plus side, warmer interior walls probably means less mould.
I believe that the main energy suppliers are being obliged to offer subsidised energy-saving measures to consumers, and I personally feel that this was a relatively small amount of money very well spent. Obviously, you have to check the small print on prices and consider the company's reputation. Also, if you have a more modern house you probably won't need it as it would have been built in.