JPG only has 256 levels for grey (or any single hue).  For highly detailed or extreme displacement, this isn't enough.  I'd suggest trying a 16 bit tif displacement map using compression for detailed or very large scale work.

You might also look at the texture filtering on your map(s), the shading rate you're using in rendering, your pixel samples, and other rendering settings.  If you are using render gamma correction (GC), you should make sure that your displacement map(s) have a custom gamma of 1.

Displacement should be used for large scale effects that need visible volume, like piping or large wrinkles on clothing.  Bump should be used for small scale effects that don't need visible volume, like fine seams and stitching, cloth or leather textures, and other surface variations that shouldn't affect the mesh.  Bump renders faster than displacement, so it's best to use displacement only when bump won't suffice.