Having just carved up this question into two different questions, I think it might be worth us in future agreeing to mark questions containing multiple sub-questions as "on-hold" until the OP or a moderator can break the questions into multiple focused questions.
Currently there are a number of problems with the current set-up:
When an OP posts two focused questions, the two can be voted up and down independently. It also means someone can vote both questions up. So there is reputation benefit for the OP, if reputation is something they care about. If they post both questions in one, you cannot vote them up independently, and they cannot get two up-votes or separated answers.
If a moderator breaks up the question, the moderator (to my knowledge) cannot assign the ownership of that question to the original OP. My usual approach here is to mark the whole new question as community wiki to avoid suggestions that I might be "stealing rep". This means that I don't get credit for the second part of the question, but it sadly also means that the OP doesn't get credit for it either.
Answers to CW questions are automatically CW. This means that when a moderator splits a question there is less incentive for good answers on that question.
It is particularly awkward when there are answers on the original question that now solely apply to the new question. They might have several +1s, but now the answer needs to be moved to the new question, and where +1s have no value, and this can feel like "stealing" rep from good answers.
This is all really manual for a moderator, and somewhat heartbreaking because I know that many of our answerers do care about reputation.
Finally, and I can't emphasize this enough, the sooner we deal with a multiple-part question, the less difficult it is to split.
So anyway, my suggestion is this: I think we, as the community, should vote to "put on hold" any question that appears to be multiple questions in disguise. This will alert the OP that something needs to be done earlier - giving them more opportunity to split the question themselves, gaining the rep for both parts of their question and saving a lot of time for moderators and answerers.
Voting to "put on hold" will also alert the moderators and other members of the community who use the "review" tool at the top of the page.
And finally, if enough "put on hold" votes are gathered, the question will stop accepting answers until it is reopened, which will save the complexities surrounding migration and/or splitting up of answers to the multipart question.
So specifically my question is this:
Should we, as a community, vote to close multiple-part questions as "put on hold" (for reason of being "too broad") until the OP or a moderator can split the question?