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Heh, I also have problems with my laptop (while on Windows XP, because I only tried there). Sometimes the sprite view background remains black or I get a periodic garbage pattern. I have a stupid Intel GMA X3100 video card, the lowest of the low I guess.
The only advice I can give is to try to get the latest drivers for your GPU. If it is still not working, you're entirely out of luck. SLADE 3 uses OpenGL for all its canvas needs (rendering any sort of 2D or 3D image) and it's not going to change.
Hum... But it works fine with sprites from other wads on the same PC (I use Windows XP too). I know nothing about it, but could be a problem with OpenGL that occours just with this sprites?