Most likely you need to be working at a larger scale for that. Edges too short for SketchUp to form them. You can see some missing faces after the Intersect at the top of the miter. That’s typical when edges get too short, too. Scale it up by a factor of 100 or maybe 1000 before doing the intersection. Better, use the Dave Method.
Don’t forget to erase that short little line segment sticking up at the back corner, too.
Using the Dave Method won’t require a change of units. Your original molding can remain at the real size you want it.
Don’t be stingy with your molding. Add a little extra before you run the Intersect operation. It’ll make it easier to select and erase the waste end of the molding afterward.
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Apologies in the picture I added in the original post, it was not easy to see the curve from that angle. Please note the white part would be the shape of the bit cutting the wood.
OK, I did more testing. The problem was the number of segments in the curve. I recreated the object from one of the faces and changed the number of segments on the curve, and it works.
I hope this helps some else, let me know if you guys think it might have been something else.