Well being a dictator you only have to worry about your approval being over 50% or so, as long as it does not go into red colour.
If you have other form of goverment the approval becomes much more important. Depending on your political party you get nice boost into abilities and also econimical boost. Also if you go to war there is going to be a vote.
The downside is that if your approval is low and you are not selected as the main political party there will be pretty serious minuses on abilities. Building approval buildings on planets with high population (mostly one approval building per farm is enought) helps you with keeping aproval on leash.