I haven't tried a one-click WP upgrade... but I think it requires that you re-install/move any templates, custom files, or plug-ins that you were using.
If you run a default installation, that's not a big deal.
If you're using custom code, templates, or a lot of plugins, you might want to take a look at the regular upgrade procedure at wordpress.org.
When you do it that way, you don't move/overwrite you content directory, config file, etc. You just deactivate plug-ins, delete the files listed, upload new files, run domain.com/wp-admin/upgrade.php, then re-activate your plug-ins.
Then just check to make sure everything looks right. If you don't run the upgrade script, things will look screwy.
Certain themes might need tweaking or updating for 2.0+ for anyone upgrading from 1.x versions.
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