Okay, there are 3 separate problems going on here based on the error messages I'm seeing.
ady, I think the initial issue you reported has been fixed. Please let me know if you experience any more errors that match the one you provided in the first post.
satanika, I think I fixed your issue. When I was querying the database for the first unread post, I was scanning all posts instead of ignoring saved draft posts like I should've been doing, so the unread post link was sometimes sending you to a draft post. Since they aren't visible to the public, it threw an error. That shouldn't happen from now on.
doubleofive, your links are throwing errors because those posts don't exist. I have no idea why you'd receive e-mail updates for posts that don't exist. Perhaps the posts were deleted before you had a chance to view them. Regardless, there should be an error message to handle such circumstances, so I'll add that. Can you tell me the date that those e-mails were sent to you?