Most problems can be prevented by following basic gas codes.
I think that a lot of people are far more concerned about the threat of deadly carbon monoxide coming from natural gas furnaces than they should be, because an 80+ AFUE or a 90+ AFUE furnace that is working properly doesn't really produce any carbon monoxide. In fact, when mom (or dad) is cooking a big dinner on a gas range with all the burners and the oven running, the results (and the danger to the indoor air quality) could be the same as operating a furnace with no outdoor venting at all.
What such furnaces do produce (like gas ranges and ovens) is a lot of carbon dioxide and water vapor. You have likely noted all the moisture on your windows from the cooking process on Thanksgiving Day. Much of this comes from the gas combustion process. And this is why more people aren't killed by all the thousands of furnaces that continue to operate throughout North America with unknown holes in their heat exchangers.