Tutorial: 3 ways to fix issues with ugly render mesh in Rhino

Various issues with rendering mesh occur when some surface is too long but thin. Dividing the long surface into several shorter ones eliminates the problem.
You can split the problematic surface into several surfaces by its isocurve (make sure that it’s not joined to the rest surfaces while doing that).
This will force both, Rhino and any other CAD program that uses the same 3 model, to generate a more dense mesh. The downside of this approach is that this surface will be no longer a single piece. If you split the surface without shrinking it in Rhino, it will preserve its original structure and could be untrimmed again in the future. However, keep in mind that some CAD programs may shrink the surfaces automatically, making it impossible to fully untrim them to the original shape.
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An alternative is to use the "! _RebuildUV" command and set “Point count=4” along the U direction (vertical direction in your case). That will add some more control points vertically and usually helps with similar mesh issues, but not always. the benefit is that it preserves the control point structure along the V direction and, if needed, you can always remove the extra added control points.
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A third method is to set a custom render mesh to the object in the Properties panel, or even global render mesh from "Rhino options, Mesh".
The custom mesh settings are used in Rhino only. Once you export the NURBS geometry to other file format, the mesh settings no longer affect the rendering mesh of the 3d models inside.
However, you can also export the render mesh, in case that you don’t need the NURBS geometry in other CAD program. You can do that by selecting the NURBS models and run the ! _ExtractRenderMesh. Then you can select all mesh models either via the '_SelMesh command or the '_SelLast command.