After straightening out UV islands, I often find that there is a lot of "Noise" in the positions of the vertices in my UV map. This results in small distortions when applying a texture to the mesh. Sometimes the "Minimize stretch" tool in the UV editor will fix this, but most of the time I just get a result like this:[![enter image description here]]
This issue is also very inconsistent. Just small changes to the geometry will drastically effect whether or not this happens. In fact, it was hard to get a screenshot of it, since adding a few sharpening loops to my mesh fixed the issue for most of the UV islands.
here is a file demonstrating the issue.