I've upgraded the blog successfully to WordPress 2.7 (with a bit of frustration). When I attempted the upgrade, I received this error:
Call to undefined method wpdb::has_cap() in schema.php on line 22
Even though I followed the instructions on the WordPress site, and I disabled all of my plugins, the error kept appearing. The only parts of the site that remained unchanged after the upgrade were the wp-config.php page and the wp-content directory. I merged the changes in wp-config.php, but the error was still present.
In frustration, I renamed the wp-content directory to a temporary name and uploaded the wp-content provided from the WordPress tarball. The upgrade completed without a problem! I deleted the new wp-content directory, put the old wp-content directory back in place, and WordPress sprang to life!
It's certainly possible that a WordPress plugin blocked the upgrade process even though it was disabled in the database.

I had to remove the "automatical upgrade" plugin for WordPress to upgrade as it should, for some reason the WordPress upgrade-system do mismatch with the upgrade-plugin.
I am having, sort of, the same issue. My issue is that I have already upgraded to 2.7, but now whenever I am in the admin panel, I get this error that you mentioned every now and then on the site but very randomly... I have went and renamed my plugins, but after a few page refreshes I don't know if the changing of the plugin folder did it or if it does it by itself..... the error that I get is
Fatal error: Call to undefined method wpdb::has_cap() in /home/nemo-maritime/public_html/wp-admin/includes/schema.php on line 22
Was randomly searching and came upon this post. Any issues of what it might be? Its driving me crazy.... but I cant get on top of it. I have upgraded, and whenever I get this error, this is what I get in the URL - mydomainname.com/wp-admin/upgrade.php?_wp_http_referer=%2Fwp-admin%2Foptions.php - then after a few refreshes I get an WordPress error page saying that my database is already up to date, and does not need to be upgraded....
Worked for me too - thanks for the tip it saved me some time!
Has anyone figured this out. Someone hacked my site, and I have the site up, but can't get into the /wp-admin part. I get this every time: Fatal error: Call to undefined method wpdb::has_cap() in /home/xxxx/public_html/wp-admin/includes/schema.php on line 22
I'd sure love to know how to fix this!