I think they are somewhat interchangeable. 'vil' can also mean 'want to' so if you are saying for example 'I will' it is better to say 'Jeg skal' because 'Jeg vil' could mean 'I want to'. In this case 'The problems want to' doesn't make sense so 'vil' has to mean 'will'.
I would also like to know this!
Update: From what I've seen, they are somewhat interchangeable, though they do carry slightly different meanings. "vil" carries more of a meaning of wanting to do the thing you're going to do, while "skal" doesn't necessarily carry a meaning of desiring to do whatever it is you'll be doing. That doesn't mean you can't use "skal" if there's a desire to do that action—"vil" just conveys that meaning a little better. Considering the sentence above, it's also very likely "vil" doesn't have to convey desire.