On an aside, I never find missing entities, until I have an Active/Training Sheriff/CoG. An Inactive Sheriff/CoG, won't find clues. So in a sense, the Sheriff/CoG squad HAS GOTTA be Active/Training. Know what I mean? It appears that all the Sheriff's squadmates share the same detective magnifying glass. If Justice system is desired, fill the Sheriff/CoG squad for best investigative reporting and results.
I have never had problems finding missing entities without a Sheriff. They are cleared as soon as a dwarf sees the corpse. However, dwarfs do not actively look for missing/dead entities, so if they never walk past a corpse, "missing" will never be cleared.
I have also seen that if a dwarf is in prison, a random member of the Sheriff's squad will be assigned to the prisoner, probably he performs the arresting/freeing or the feed prisoner job. Might be the latter, as that does not seem to happen with vampire prisoners.
To get this as accurate as possible we will have to differentiate the different noble tasks into further categories, as some task might conflict with being in a sqad while others might not. Like this:
Broker: Enables wealth display (passive); Trades at Depot (active) <- in this case the passive task does not interfere with being in the military, the acive one does
Manager: Enables Workshop Profiles (passive); Job Assignment (active)
Bookkeeper: Enables Stock Screen (passive); Updates Stock Records (active)
Chief Medic: Enables Health Screen (passive); Diagnosis is NOT a Noble task, any dwarf with Diagnosis enabled can do it. If the Chief Medic is in a squad, but there are other Diagnosers, there is no conflict.
Hammerer: Executes prisoners (active); possibly does not interfere with being in an active squad
Militia Commander: Enables Military screen (passive)
Militia Captain: Enables Squad menu (any squad leader does)
Sheriff/Captain of the Guard: Enables Justice Screen (passive); Arrests/Beats criminals (active); active task does not interfere with being in a squad, possibly needs to be in a squad to perform task
Mayor/Expedition Leader: (needs to talk to people to perform task, so I classify his task as active) Receives complaints from unhappy dwarfs (active); Conducts Meeting with liaisons and diplomats (active), before there is a baron
Baron/Count/Duke: Conducts Meeting with liaisons and diplomats (active), he will take over this job from the mayor; Appoints Champion (passive)
King/Queen: No task (according to the wiki he is supposed to appoint the General, but AFAIK Generals do only show up if they are the spouse of the king/queen)
General: No task
I am very sure that King and General have no task, I have had them in forts for many years. Even peace agreements were done by the Baron.
Champion: Talking to the champion gives dwarfs "talked to a pillar of society" thought, depending on the dwarfs attitude towards authority this is a minor happy or minor unhappy thought. He needs to talk to dwarfs to give this thought, so if he is not in a squad and idle all the time, every dwarf gets it, if he is in a squad and training full time I think only dwarfs that train with him get it.