A comment directed to popular demand, posted and deleted in my question about high rep users is still in my and popular demands' global inbox.
Additionally, edits do not affect the global inbox.
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Deletions are now reflected* in the inbox.
There is, of course, a natural race condition; wherein you load a page with a notice right before the originating user deletes the answer/comment. That's not going to be addressed.
As for edits, we're unlikely to ever reflect those in the inbox. Its a lot of trouble (technically), when you're almost always just going to go and read the post/comment.
*This is "going forward," old items that are in the inbox that correspond to deleted posts or comments will remain. At least for the time being.
Update 2011-02-20 — This seems to have been fixed again?
Update 2011-03-26 — No, not fixed.
Update 2011-05-04 — Ah, Grace explained that only deleted comments to posts that you own persist in the Inbox.
Indeed, this annoyance has been back for some time. Some examples, just in case it helps:
My Inbox shows deleted comments, when I already read them in the post before they were deleted (old example, not currently shown):
... and also when I did not read them in the linked post before they were gone (comment 190060):
Same texts in meta.stackoverflow.com/inbox, but I guess that's the source for some Ajax magic that populates the actual Inbox.