Blizzard lists known issues with StarCraft II, updates system specs
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Blizzard has posted a list of known issues for StarCraft II over on the official forums, and other than current bugs, there's also more detail on what processors and video cards will/won't work with the game.
Just launched today, StarCraft II's issues are bug related, one of which is the game's auto-updater being shown by anti-virus programs as a Trojan, and another showing black screens "being related to the use of a Quick Cam webcam."
A couple problems have workarounds listed, so hopefully those will help you eliminate the problem until a fix is issued.
The PC specs confirmed by Blizzard earlier in the month were also updated, so you'll want to double check the system specs before running out and buying the game.
Thanks, BigDownload.