What are the advantages to Harry not having known how special he is before he starts school? Disadvantages?

Assuming you're referring to Harry Potter, then I would say:

Advantages to Harry not knowing how special he is before school starts: he didn't have that weight on his shoulders, that anxiety of wondering how the other students would react to seeing him, and he expected to be like any other student

Disadvantages to Harry not knowing how special he is before school starts: because he had those expectations of being a normal student in the first place, he was caught very off guard when everyone started making a fuss over him, and he wasn't prepared and didn't know how to react.