Yes, that makes sense. The construction 'was going to get solved' is grammatically correct. If I were saying this, I might save a few words and simplify it to this, for example: 'I was hoping this problem would be solved by the recent update.'

I'd sooner use "would" instead of messing about with "going to" (remember that your first verb is "hope" - that does affect which verbs you can use, and in what form). The use of "get" is also out-of-place; too colloquial. "I was hoping that this problem would be solved with the recently-issued update."

Maybe because it's past continous.