You only need to adjust Min Displacement Bounds when the renderer is unable to guess what value to use. The way it works is that when doing ray intersections, the renderer is trying to optimize by skipping objects that are so far away there is no way that a displacement could cause an intersection. In certain rare situations, the shader can be doing something tricky that results in larger displacement than is directly evidenced by the root node displacement parameter value. In such cases, you can see mysterious gaps in some polygons as if the renderer didn't "see" the moved pixels due to displacement.

If you're not seeing gaps in the mesh caused by excessive displacement beyond the amount the renderer was guessing it would find, then you do not have to set this, ever.

Conversely, setting this when you don't need to does in fact slow your render down. So if you ARE setting it, it has to be for a good reason, otherwise you're canceling the optimization that the renderer is trying to use. The value overrides whatever the renderer thinks is best, and instead tells it "try harder to find intersections this far away even if you know that isn't going to happen". Like so many advanced settings, the value not only does some good occasionally, but also does some serious harm. Don't change things unless you know exactly why you're doing it.

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Renderosity forum reply notifications are wonky. If I read a follow-up in a thread, but I don't myself reply, then notifications no longer happen AT ALL on that thread. So if I seem to be ignoring a question, that's why. (Updated September 23, 2019)