Slugs are common in gardens in the West. In common parlance calling someone a slug would be like saying someone is icky. Icky as in slimy, covered in slime. Slimy things are things many people seek to avoid as they evoke an entire range of distasteful subjects, etc. (Personally, I actually love all those funny garden creatures.) Also, a slug is considered to be a "lowly creature" unlike a butterfly or rabbit. In addition, a slug is considered to be brainless.
It is here a kind of childish way to insult someone. After all, Rowling wasn't going to say that the Dursleys thought of Harry as a shit. But, in fact, they did. Look how they treated him. The Dursleys are the embodiment of everything negative about the middle layer of the middle classes who try to act like they are better than everyone else. Just like in the British comedy series "Keeping up Appearances"
It is actually pretty funny.