The origins of the edge problem is that one of the surfaces that meet at that corner is not long enough to reach the corner. Its just a hair short. There is also a tiny little surface in the corner that may have been the result of trying to fix the problem. The tiny surface is also not big enough to cover its trim boundary and shouldn’t be there anyway since as a trimmed surface it is much smaller than your file tolerance.
So delete that surface.
The only good way to fix something like this is to untrim the surfaces with bad boundaries and redo the intersections and then trim and join.
In this case the surface that is short needs to be extended by at least 2 or 3 times your absolute tolerance (>.002"). When you untrim you can preserve the edges so that you only need to replace the one edge where the 2 surfaces intersect and then after you fixed the boundaries of both surfaces then you trim and join.
NakedEdge_FAILx.3dm (543.7 KB)
Of course, Rhino should be able to diagnose the problem and do all this work for you, but don’t hold your breath on that happening anytime in the near future.