Once installed, corrections get sent directly to WordPress' dashboard, where administrators can then make a fix just like they would approve or deny a user comment. Because the plug-in is given privileges to write over your content, it then goes back into the post and makes the edit, without the administrator having to do it manually. Best of all, it shows you a before and after preview of what the correction would look like, so you can eyeball it without having to visit the post in full.
To aid in the correction process the plug-in supports multiple administrators, meaning a multi-author blog can decentralize who has to take a turn at the copy desk, and can pass off the responsibility if one of the members is out of the office. The plug-in also throws in a few nice tweaks like a complete history of suggested user corrections, and a summary of your blog's accuracy rating, which gets updated with each user-requested fix.
GooseGrade is working on a public API so others can come in to make similar tools, so expect to see similar plug-ins for other blogging platforms in the near future.