Most folks who design/build masonry stoves strongly recommend an outside air source. This means that air is drawn directly from outside the structure through a dedicated pipe that dumps directly into the base of the appliance. I believe most conventional wood stoves recommend a similar setup. In some locations this is actually part of the building code, so depending on where you are, you may not be allowed by local code officials to install one of these without the outside air source.
The purpose of dedicated air sources is to provide adequate O2 to the fire without depleting O2 in the home. It also ensures that the stove has proper air flow in today's tightly sealed homes. That way the stove will draw properly and you don't have the spectre of carbon monoxide emissions into the home. Of course, with a masonry stove the supply line and the chimney generally come with shutoff valves so that no air (especially cold, outside air) is drawn through the stove. This step saves the heat that has been stored in the masonry. The only drawback of this system is that you must remeber to open the damper and the inlet before you try to light a new fire.
I don't think a properly installed and vented wood stove or masonry stove should present any problems in a dome as long as the occupants follow all of the basic rules pertaining to wood burning appliances. It is a good idea to install an O2 sensor in the home too. Doing so would provide a warning system for the eventuality that somebody didn't do something correctly or the appliance is not operating properly. Again, this may be a code requirement in some areas.
I believe all of these precautions also pertain to any heating appliance that uses fuel whether it is natural gas, heating oil, or wood. Of course, electric or solar provide heating without this worry, but they are not always practical and nothing beats the warmth of a wood fire on a really cold day.
I say , if you want a woodstove, go for it, but take some precautions.