Mods are outnumbered, and the few of them on SO (relative to user base) probably spend a lot less time browsing questions -> following links than us commonfolk. If I see a post with a broken link, I might look around near the link's location for the intended content, but if I can't find it, I edit the link out, and the description says so.
If anyone wants to go through the edit history to find the original link, and do more thorough searching, have at it. But I don't think we ought to just "flag" a post for a moderator to fix later. It's removing a link; we can all handle that work ourselves (rather than push it off to someone else).
And as Sam said, this should be tackled, because nobody wants to crawl through posts all day removing broken links. The link checker is a great idea. But that's a separate feature request; until it gets implemented, can't we collectively handle this?
My opinion: low-rep users ought to be able to do a special kind of edit - specifically for reporting broken links - that, like a normal edit, needs approval, but only from decent-rep (say 2,000, the same for instant editing) users, and mods aren't bothered by it.