For these irregular vertices, we only have C1, not C2 smoothness

Is there any way to rid of irregular vertices or is it ok to have many vertices with different degrees? What makes a "good" mesh?

Going off of the previous questions, I'm wondering how we might go about transforming a vertex to have degree 6/ if this is possible. Do we need to smooth these points, or add more sample points in their locations?Also what is our method of tracking vertices with degree unequal to 6? Also why 6?