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Cyan comments on The First Step is to Admit That You Have a Problem - Less Wrong
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I don't think that's it. The distinction between tasks and problems is well-expressed in the idiom of Eliezer's post on Possibility and Could-ness: achieving the GOAL state is a problem until the could-ness algorithm has managed to label it "reachable from START", at which point it becomes a task. (This makes the problem/task status of any particular GOAL a property of the current state of the could-ness algorithm, which is as it should be.)
I think Alicorn intends to offer observations which might improve the execution of our could-ness algorithms. The current post points out that due to the similarity of language we use to describe tasks and problems, it's common for people who have problems to fail to recognize that fact and not even start their could-ness algorithms.
I think the reason for the common lingual similarity in treating problems and tasks is the ACTUAL similarity. Could-ness, or reachability of a theoretical (alternate past or unknown future) world-state is not binary. It's a probability function related to likelihood of theoretical actions and likelihood of various results of those actions.
If your could-ness function returns one bit of information, it's too simple to be very useful. And any theory of decision-making based on it is equally oversimplified.
I do think there's value in exploring this as a (false, but perhaps novel) quantization. Choosing between physical movement vs searching for alternate plans vs abandoning/altering goals (all of which are action, but feel somewhat different) is a real part of any decision theory.
I don't think the quantization is real. The chose of what to do next (perform some physical action, think about alternate strategies, or rethink goals (or change focus to a different goal)) is valid and necessary for things labeled tasks as well as those labeled problems.
If you want to consider probabilities other than epsilon and 1 - epsilon then the distinction becomes: setting up and approximating the solution to the right Bellman equation is the problem stage; carrying out the indicated actions is the task stage.