Regarding carbon-14, there is so little of it that it makes no sense to even think about it (about 1 in 10^12 atoms). In addition, all biological matter (including you and the food you eat) has carbon-14 present in it -- that's the basic principle behind carbon dating. In fact, ash from wood burning would probably have more carbon-14 if anything.

But yes, the article you linked talks about trace amounts of uranium and other materials that actually could be harmful.