I've been able to use Safari no problem.
The biggest issue is that you set it up to accept cookies... and not to cache pages. That'll fix any issues (but those rules apply to any browser/any platform).
Also make sure your clock is set correctly, and that you are using the same domain name througout your site.
In other words don't use
www.yoursite.com interchangibly with yoursite.com (no www). This confuses things because it's possible to be logged in at
www.yoursite.com, then click a link without the www and you are no longer logged in.
Hope that helps.