Carbon dioxide is an atmospheric pollutant. Incomplete combustion produces other pollutants.
For example, here is one possible equation for the incomplete combustion of propane:
propane + oxygen → carbon + carbon monoxide + water
C3H8 + 3O2 → C + 2CO + 4H2O
The carbon is released as fine black particles. We see this in smoky flames, and it is deposited as soot. Soot can cause breathing problems and it blackens buildings. It may block boilers and other appliances, or cause a fire.
Carbon monoxide is a toxic gas. It is absorbed in the lungs and binds with the haemoglobin in the red blood cells. This reduces the capacity of the blood to carry oxygen. Carbon monoxide causes drowsiness, and affected people may fall unconscious or even die.