Visual display of edges will not be good until you change the Edge Quality from the default Medium to High or Very High. In 2001 the choice is View>Display Settings>Model Display>Edge/Line and change the quality. Another factor in how edges are displayed depends upon the accuracy you are using. I would not suggest changing accuracy unless absolutely necessary.
Maybe the reason your tangent edges are not displaying properly is you have geom checks. The way to possibly fix it is to change the accuracy to something higher. If your model is good all should be well.