Apart from being harder to clean in the long run, a dirty oven can affect your food in a negative way. The continuous burning of food leftovers in a dirty oven can develop carbon-based fumes. These fumes can change the taste of your food or anything else you are preparing with the oven.
The smoke released by a dirty oven is also bad for you; it can contain harmful gasses such as sulphur dioxide, nitrogen oxide, and carbon monoxide.