How to finish Master's Thesis when my adviser is too busy to help me thoroughly edit what I have written?
It sounds like you have two major concerns about getting quality feedback from your advisor: (1) he's busy, and (2) he's not as familiar with your new topic. I'll address these separately.

Getting high-quality feedback from someone very busy

To get the best feedback possible from your advisor, make sure that whatever you send him to review is as polished as possible. If he's pointing out typos and areas where the writing has issues, he's not going to have as much time to evaluate the content, which is where his feedback is most valuable. 

It will also help if you identify and tell him about the areas where you think you most need extra high-quality feedback: "Could you tell me what you think of the formulation in Section 3, I'm not so sure about that part."

Getting high-quality feedback from someone not an expert in the topic

Even though your advisor is not an expert in your new topic, he's an expert in something and he knows what good work looks like. He knows when an argument seems weak and "hand-wavy" and when the evidence on offer doesn't support the claim.  So he's still likely to have good advice even if he isn't as familiar with your topic as you would like.

In fact, for PhD students at least, it is generally assumed that the student knows more than the advisor about the thesis topic by the time the student is about midway through the program.

On crowdsourcing thesis feedback

Having said all that, it's still useful to get comments from others in addition to your advisor. 

Ask your friends to read your thesis to (1) find typos and obvious mistakes, and (2) note areas where they think something is unclear, so you can improve the writing. This will help you make sure the version you send your advisor to review is as polished as possible, so you'll get better feedback from him. 

If you know some professors who are expert in your topic, you can send them a copy, but follow the advice for getting feedback from someone very busy: Make sure what you send them is very polished, and identify where you want their help the most. If you don't know any professors who are expert in your topic, then after your advisor gives you his feedback, ask him: "Do you think we should also send this to an expert in the topic for review? If so, do you know anybody we could send it to?"