I assume you tried reinstalling the game?
Someone with Win 7 64 and an ATI HD4870 reported occasional graphical artifacts (with the UK or Australian version of the game), which they fixed by running the game as administrator and disabling desktop composition. Maybe that would help? Right click on the D2:ED shortcut, select Properties and switch to the Compatibility tab.
The game does not support crossfire, so you could try disabling it (some people have also renamed the executable to get the drivers to use the associated profile for another game).
Crossfire Support for D2
