It would appear that Google/Blogger have either inadvertently introduced a serious bug to their comment system or they've added a feature intended to drive popular blogs away from using "Anonymous" comment posting.
It now appears that if you are not logged in and view the comments in a Blogger blog then the system will allow you delete any comment on someone else's blog if it is either (a) Anonymous or (b) has a Name/URL entered by the user.
The following screenshot was taken in Epiphany whilst not logged in to Blooger. You will see that I had the option - via the little rubbish bin - to delete comments on my blog even though I was, in effect, just an ordinary person browsing the site and should have no access level to do it.
This is what appears after you delete a comment that is either anonymous or simply filled in with a Name/URL.
That's like an epic fail on Blogger's part if it is not a deliberate move to get people registering on sites.
Feel free to start deleting any of the comments that you can on this blog if you must. I don't really mind.
Update: Tracking suggests the nice people at Google now know. Perhaps they can mail me when its fixed?
Update II: Word reaches me that Google are on it. What that means I don't know.
Update III: For anyone wondering what this bug is actually doing, it seems to be that Blogger is assuming that a comment that is not made by someone logging into a formal ID handle is "anonymous" therefore anyone browsing the site without being logged in is "anonymous" too, ergo you are the author of the anonymous comments on all Blogger sites. Nice!
Update IV: This bug was fixed by Google with a rollout of new code Friday afternoon. Apologies for the late update.