Everything that is red is overlapping UV’s. I suspect that when you created the UV mapping, some parts of it went outside the 0,0 through 1,1 UV space. The result is that you get overlap. You were actually lucky to be able to create a displacement map at all! Normally, the computer rebels when you try to write two different values to the same texture pixel, with the result being that the program crashes.
There are three ways to fix your problem. One is to remap the model in your other program, being careful to keep everything in the 0,0 through 1,1 space. Another is to remap as above, but deliberately break things up into different spaces. You would then use Mutli Displacement 2 (part of Displacement Exporter) to create multiple maps; one for each UV space. The third option is to use ZBrush to remap the model. At level 1 you would assign a blank texture to the model (such as 2048x2048 or 4096x4096) and then press Tool>Texture>GUVTiles. You can now create a displacement map without problem.