1) Clip any pixels that have their texture coordinates extend beyond the heightmap boundary (texture coordinates cannot go outside [0,1], or whatever other range you want). This can also be specified per-vertex for added adjustability.
2) Render a box instead of just a plane. This will allow the front edge of the height map to be rendered as well.
Here are the results of the first part:
![](http://members.gamedev.net/JasonZ/Parallax/mited_parallax_occlusion_mapping_planes_100001.jpg)
I think it turned out pretty good...