Many good ideas in this thread, but i think live missing dwarves should operate mostly internally, with overseer reports ocurring only if the missing dorf is stranded/walled in. Some thoughts.
1) I love the idea of having sheriffs/fortress guard be responsible for finding missing dorfs, since missing dorfs are potential crimes, which are their responsibility.
1.1)In fact, since they are the fortress' internal security, it would not be a stretch for sheriff/fortress guard to periodically engage in "patrol" tasks where they actually go around the fortress, keeping tabs on dorfs, asking questions (thus learning who the questioned dorf saw) and maybe even catching crimes red-handed. Thus, they are more likely to know the location of most dorfs and resolve missing reports immediatly. This will also incentive large fortresses to assign more people to the guard if your captain is spending most of its time patrolling a huge fortress alone. (ninja'd by chthonic :p)
2) Regardless of how the missing live dorfs are implemented, i dislike the idea of hiding missing dorfs from the player's view. Missing reports could serve as valuable warnings that a dorf is walled-in/stranded, and hiding the missing dorf only makes his rescue more difficult. At most, make it impossible to zoom in creature the missing dorf on the unit screen, but it should be visible on the main screen and obey orders as normal.
2.1) Basically, this could make the sheriff/fortress guard work as a unit-list analogue to a record keeper. If you ignore it or put too little time/dwarfpower on it, you will have lots of missing reports and lose the precious ability to zoom in on the missing dorfs.
2.2) What i worry about is the announcement spam. All of this missing dorfs systems needs to be balanced to avoid excessive announcements.
I think this is a good idea. Totally losing control of any group of dwarves, especially those that you definitively want to be kept separate from the rest of the populace but still control, would be a problem. You could have dwarves that the majority of the populace doesn't know are there, but you're still aware of them yourself because they're aware of one-another. The buddy system.
As Evile just pointed out, guardsmen/sheriffs need to go check their last known location. Hopefully Toady would see the need for implementing tracking and trails at that point, so the guardsmen can hunt them down. And the use of meeting zones to reset the missing timer is a good idea as well.
The question though, is determining how the player actually views the world. To have dwarves worried about their acquaintances going missing I could accept, and to have
announcements depend solely on what the dwarves know is also acceptable. But other than that, I would see little value in taking away the player's omniscience regarding our ability to see everything going on in the world.
For instance, if the player's perspective is that of the dwarven government, then we'd almost have to take a purely first-person perspective where you have absolutely no idea what's going on unless the mayor can see it happening or be told by another dwarf he respects.
If we're a god though, then it would make sense that we know everything about what's happening on screen, and everything your dwarves know, but nothing that neither your dwarves know nor is happening when it isn't actually on screen.
If you SAW Urist McGoodVictim being murdered by a vampire, then there would be no question about it and you could act immediately, but if the dwarves don't know and you didn't see it happen, then you have to wait to find out about it.
This would have to go for invaders and other creatures as well: they may search the fortress for things to kill, but unless they interrogate Urist McSocialite (and he caves), they wouldn't know of any dwarves they cannot see. Then, if they have covered every accessible space of the fortress and can't find any clue to where the survivors could be hiding, they would start to settle in. If they do find evidence of places where dwarves could definitely be hiding, such as a locked hatch on the floor above them where the trolls can't bash it in, then they could blockade it/use their tunnelers to make their own entrance, and possibly begin settling simultaneously. You could end up seeing the goblins moving into your fort and/or looting it while your few survivors are locked away in a well-hidden cell. Then the question becomes how the outside world treats it; if they now understand it to be a goblin-controlled fort, you wouldn't get migrants, other than goblins, but possibly dwarven armies, or others that want to siege the goblins. You could also engage in guerrilla warfare with the goblins to take back the fortress.