Edit Comments XT is a simple WordPress plugin that allows commenters to edit their own comments. To edit a comment, a user must have the same IP address as the user that made the comment and they must also make the edit within a specific time frame. The default edit time window is 30 minutes, but it can be changed easily in the plugin’s option page.
If you’re logged in to WordPress, it will use the more feature-enhanced wp-admin comment editing screen, but if you aren’t then it will just allow you to edit the content of your comment. It’s a good idea to test the plugin from a logged-out view as well.