ergophobe - 4:23 pm on Oct 28, 2010 (gmt 0)
Lorax is right - this has nothing to do with the operating system the server runs on. PHP runs fine on Windows and there are very few differences. I've created dozens of sites on Windows and ported to Linux without ever a problem.
In your case, you are getting Notices. There are basically three levels of reporting in PHP - Errors, Warnings and Notices.
Some neophyte developers create their themes, plugins and apps with error reporting set to hide notices and someitmes even warnings. This means that if you are using an environment with error reporting turned up a notch (which you should for development), you'll get these notices. To me, it's a sign of poorly written software by a careless developer.
Now, *which* developer? Not Wordpress. I can assure you that it runs fine with the highest error reporting. I don't use Thesis, but I'm sure Lorax can confirm that it runs without notices in a default install.
So I would from there I would disable all plugins and sidebar widgets and revert to the default theme as Lorax says. Then reneable one at a time until you get the Notices. Then see if there's an updated version of the offending piece.