The appearance of dashing for your line is because the line is running alongside the surface in those places. As a consequence is it going in front of and behind the facets that comprise the plotted surface and thereby becoming obscured when behind the surface and visible when in front of it. To see this, if you add the Option

ContourStyle -> {Opacity[.5]}

to your ContourPlot3D for plot1, it will become apparent.

It's kind of hard to avoid if, as I think is your case, the curve you are plotting is the intersection of another surface with your original surface. One possible approach (though this may be hard to implement consistently along the whole curve) is to add a small translation to the curve to move it away from the surface.

Here is a Manipulate using your expressions from your code to see how this might be done:

Manipulate[
 Show[plot1, plotadd /. z : Line[___] :> Translate[z, {0, a, 0}]],
 {{a, 0}, -3, 3}]