GTD & Project Management Methods
Gideon,
From a GTD Point of view a Problem usually leads into a project, for example a problem may be that the Garage is untidy and needs to be cleared out which would be captured as a thought as part of the capture phase.
A Project would then be created when time/energy available - Garage Tidy Project, next actions might be to sort through a cupboard, then to put identified trash out, stuff that could be sold/ebay'd, etc.
You could also think of this in terms of the Problem being the Objective of the Project.
From a Project Management Point of View, a problem could be something unforseen when the project was started, which would then be managed using an issue log, which would detail what the identified issue is, , what the impact of that issue is and what countermeasures can be put in place to reduce the impact or risk on the project.
As an example, computer hardware/software required for a project is being quoted on a longer than average leadtime from the preferred supplier, which would be the issue. The impact would be a 2 week delay on the project, countermeasures would be try to source from an alternative supplier or source an alternative product.
Hope this helps.