It appears that it is only possible to link one problem to an incident. Most other links seem to allow for a many to many link, for example many incidents can be linked to one problem, many configuration items can be linked to a change, etc.
We have situations where we use an incident to ask the person within the department that does purchasing to order equipment, and if I'm trying to bundle a request for multiple failed items that each have their own associated problem I can't link all those problems to the incident that I create requesting the equipment be ordered.