This is a hard question to answer, because all citizens are different. However, I would say that there are a few views out there.
First, some cynical citizens may view diplomats as doing nothing of value. They may come to this conclusion based on the troubles of the world. There is a lot of social unrest wherever you look. Think of what is happening in Syria now and the Arab Spring last year.
Second, some may hold the opposite opinion. These people may view diplomats are very important in keeping peace and understanding among the nations.
Third and most likely, the majority of people hold a view of what diplomats do to be somewhere in the middle. Diplomats are necessary in helping nations understand each other, but due to the complexities in the world, diplomacy is limited and often times stymied.