Incomplete combustion occurs for a number of reasons. It can be due to an incorrect amount of air being included in the purpose, technically referred to as Lambda < 1. The main reason is a poor mixing of the available air with the fuel being burned. This is naturally not always easy. Gaseous fuels can be mixed fairly easily and liquid fuels can also be atomised reasonably well if heated and placed under sufficient pressure, but solid fuels are more difficult. Large coal-fired burners, such as power stations will powder the coal first, and then add it to the combustion chamber in a fiery waterfall from the top, very impressive to watch! Smaller systems are more limited in their possibilities, and this is one of the areas that receive a lot of research work.
Improving fuel mixing and hence combustion can make a large difference to the success or failure of a fuel type as a mainstay of energy supply. Incomplete combustion leads to smoke and soot formation, as well as the production of highly toxic carbon monoxide. Generally, the carbon and hydrogen atoms that are no combusted will combine together to form methane and so be detectable in the flue gas stream.