This is an interesting question.

Responding sideways, I can give a closed exposition problem, namely the Kepler conjecture. Here is a talk by Thomas Hales:

Lessons learned from the Formal Proof of the Kepler Conjecture

I think it makes for interesting watching. Part of the jist of talk is that the first proof, the one submitted to Annals of Mathematics and which took seven years to referee, was difficult even for specialists. This wasn't just down to the immense amount of computational data that the proof relied on, but was also down to the nature of the proof itself. When Hales came to rewrite it in order to make it amenable to formal treatment, he was surprised to find out how much time he spent in math land (to use his words). New insights were had, in fact other outstanding conjectures were settled as a by-product of this work. The resulting new proof Hales calls the blueprint proof, and in all respects it is a very different one to the original. It is more structured, shorter, and simpler.

If someone suggest tackling the original proof I would run a mile. But the new, blueprint proof? I might read some of it one day and I am hopeful that its lower reaches would not be beyond me. In short, I'm not intimidated by it. So I would say that the Kepler conjecture used to be an open exposition problem but now, because of the blueprint proof, it's closed!