AndyA - 3:18 pm on May 18, 2012 (gmt 0)
Hi backyard and welcome to Webmaster World.
It seems to me that your ability to delete comments depends on the app used to post the comment. You should be able to remove the comment from your Timeline on Facebook, but the ability to edit or delete the comment itself most likely lies within the configuration of the app used or with the site the comment was posted on.
Some of the apps on Facebook ask for too much personal information, IMO. I'm to the point where I won't use many of them, because I don't feel it's necessary to provide them with a list of friends, phone numbers, etc., just to post something on my Timeline or leave a comment.
If you are able to contact a moderator at the site where the comment was posted, you could ask them to please remove it. Other than that, I'm not sure what other options you may have.