Looks like a video card issue to me. You should check to make sure your drivers are up to date, and in the mean time, also post this to the D3 technical support forum.
I have the SAME exact problem and nobody seems to know what it's about, i have a Radeon x1950 pro which is on the list of low settings drivers. you're not alone in this
i almost have the same thing as yours but to a minimum extent, as only all shadow parts of the game are all turned bloody red.. im running an ati mobility radeon hd 5650 it is almost ok.. but still a number of glitches.. you are not alone
Post these kinds of problems on the technical support section of the D3 forums. You will be more likely to get support from folks with IT experience, and other players who might also have had a similar problem :)