I am getting the same errors with ONLY this plugin installed using the default WordPress theme, so I'm pretty sure this is not due to a plugin/theme conflict.
When activating the plugin, the "Tumblogs" where you can view the taxonomy is completely missing. I'm able to bring it back by changing the options from "post formats" to "taxonomy" back to "post formats" again. Once I do that, the "Tumblogs" link shows up, However, when I click on it, it results in this error:
In addition, after trying to do a Tumblog test post from the dashboard, I noticed it only schedules the post rather than actually publishing it.
I have never seen a plugin give such perplexing errors. Any help in resolving it is appreciated, as I really want to get tumblogging functionality. I am using the latest version of WordPress. (3.1)