I am having the same issue. None of the techniques on the troubleshooting page (
http://www.gog.com/en/support/broken_sword_directors_cut/_i_b_read_first_b_common_troubleshooting_steps_i_ ) worked for me. I still get slow and choppy animation, a mouse that will barely move and has a hard time selecting things, and blank white backgrounds once I manage to skip past the intro animations.
I am running Windows 7 64 bit, with a NVIDIA GeForce 9800 GT graphics card (with the latest drivers), and an AMD Phenom II X2 550 Processor.
EDIT: OK, the choppy animation problem has been SOLVED! At least, for me. I right-clicked on the exe (or shortcut), and went to the Compatibility tab. From there, I checked the box marked "Run in 640x480 screen resolution." The results were night and day. The graphics still aren't perfect -- the panning is a little choppy, the mouse movement doesn't feel 100% smooth (I'm not sure it should, running in 640x480 on a hi-def monitor), and I'm noticing some mild V-sync issues ... but that might just be the age of the game. In any case, I'm considering the choppy animation/mouse issue solved for now ... even if it's not as smooth as a modern game would be, it's now PLAYABLE.
Unfortunately, I've still got the blank white backgrounds! Investigating other threads for possible solutions to that one...