Permissions to get autoupdate to work

I’m at version 3.0 and want to move to 3.0.1 without having to download>unzip>delete>upload but I get this error when trying to update:

Could not create directory.: /public/wp-content/upgrade/wordpress-3.tmp/wordpress

Is it safe to chmod 777 the upgrade folder?

It should be relatively safe to chmod it to 777 for as long as you need to in order to upgrade, and then change back to what it was before. Generally speaking, 755 is the recommended directory permission.