There’s an argument to be made for cleaning your heat registers…actually, there’s several.
First, there’s the energy argument. In theory, especially in forced air systems, air flow is reduced as heat or air registers become clogged and otherwise dirty. Anything that reduces airflow has the potential for jacking up your energy bills because the furnace (or a/c for that matter) has to work harder to attain the desired room temperature.
And for non forced air heating systems (radiant heating for example), if the heating apparatus is dirty, the furnace (or heat source) …

Unfortunately, there is some bad news that comes along with sealing windows, walls, and doors that may leak. That something is air pollution or contamination within the home. By sealing cracks, you’re saving heat but also giving pollutants less opportunity to escape your home. Carbon Monoxide, an odorless, colorless and very poisonous gas can also be trapped.
To reduce this risk, make sure you change the filter on your furnace often, preferably with a premium one that stops as much allergens and particles as possible. Be especially vigilant if …