Quote Originally Posted by Throbert McGee View Post
Possibly кое- could be understood as "specifiable, yet for whatever reason, left unspecified." (Like if you say "I saw a certain someone yesterday" -- the "certain someone" is in fact a specific/non-hypothetical person known to the speaker, but the speaker just chooses not to state who this someone is.)
Yes, that's the difference. "Кое-кто"/"кое-что" are used for people and objects whose identity is known to the speaker, but who prefers to use a pronoun anyway. Knowledge doesn't need to be comprehensible: if someone walked into your office looking for your colleague (who is absent), you are certain to use "кое-кто" when your colleague is back if this person left his/her name or something. "Кто-то"/"Что-то" is for people and objects that you are pretty sure are/were/will be there but you don't know their identity.
In a sentence like "I need someone" you use it like "Мне кое-кто нужен" if it is a specific person ("I'll tell you in a moment who it is") or "Мне кто-то нужен" if anybody will do ("Just need a man or two to start working on this").

"-нибудь" series of pronouns is used for uncertain "anythings" that may not even exist. That is, they are good for asking "if anything happened", unless it seems like something HAS happened (you may use "что-то" in this case). But you cannot use them in strictly positive sentences in Present or Future tense: for example, "Someone is waiting for you at the couch" or "He is carrying something". In these sentences you are implying a person or an object exists, so it makes no sense to tell "maybe not". Of course, it changes for hypothetical sentences ("If anyone has any objections...") and questions.