I wouldn't for the cart and checkout, I would actually no-index them. The reason being is depending on what measure you are using for cart abandonment, having people land on those pages will skew your results. Also at the same time there is no good reason for them to enter on those pages so it will increase the overall bounce rate if people are entering on them.

Privacy policy, shipping, and return policy, I would not specifically no-index them, but I would not try to optimize them for anything other business name - page name. That being said, if you are like Costco and offer some amazing return policy that someone can return a product after 10 years for a full refund and it is a popular product; I might consider optimizing the return policy for that as well. Or if you are the only person that offers free international shipping on a large item like a baby grand piano or something. But if you fall in line with the rest of the industry I would just leave them as is and only optimize them for your business name - policy type. So then if people search for your business and return policy those pages will more than likely come up.

Personally I haven't had it happen to me, but I have heard a lot about it. I think the main thing us as SEO people have to consider is that Yelp is a paid service. Their only real revenue stream is from businesses paying them for advertising. That being said I hear they exercise a lot of liberties with these businesses and their reviews that other companies do not exercise.

All and all Yelp is pretty scummy, someone really needs to take it to a point and sue them. They try to extort companies by making bad reviews go away if you pay them. They also make good reviews go away if you don't pay them.

These are my main points.

If my links are taking me tweeting them to get added (some are over a year old with good PA) then my competitors need to tweet their backlinks as well. But if they do not know to do that, then the Mozscape that I am looking at for my competitors is seriously out of date as well. If I start noticing positive changes in their sites, I cannot do any kind of research with Mozscape, since the index is outdated.

About your first crawl statement. What you are saying is there are two indexes, correct? One index that has pages with PA and DA assigned. Then another index of pages that have actually been crawled. Then you merge those indexes to make the Mozscape index and pages with PS and DA that have not been crawled are just orphaned and used for the toolbar.

What factors decide whether a page is crawled or just assigned a rank?

And how can Mozscape be deemed accurate without actually using referral url information?

Generally it is against Google's guidelines if you are buying a do follow link. So in doing something like this you need to weigh the SEO vs Marketing value. I personally do it with a lot of my clients, but not for SEO purposes, it is for marketing / sales purposes. My clients are generally e-commerce sites for a little insight. See some markets have blogs that people read every time it is posted. Kind of like a Rand Fishkin article in our market. If Rand came out tomorrow witha whiteboard friday and said this product is great, it boosted Moz's organic SEO by 100% think how many people would flock to buy it. Most of the time since paid links should be no follow, there is no SEO benefit, but at the end of the day if it puts more money in yours or your clients pocket than was spent, then it is worth it. I will say that I buy links, I make sure they are not followed and I buy them when I think they can create sales for my clients. As far as I know that model fits in the Google guidelines because buy making sure they are not followed I am not buying them for SEO purposes.

I personally think there is a lack of them and would be interested. I do not know if you are familiar with ecommerce fuel, but they have a forum where everyone is screened and pays $25 a month to be a member. I would be interested in something like that, because it keeps the knowledge level high in my opinion.

If you are using the new bar, on the left hand side click the marker next to the page with the magnifying glass. From there you can highlight links.

Frankly, I believe in calling a spade a spade. I did misspeak on the issue though. Because of so many complaints about how they do their review system they are being sued in a state supreme court right now. http://investorplace.com/2014/04/yelp-stock-charts/#.U6xgBfldVHQ  But, that is beside the point to your issue.

From what I have learned they have an internal "rating" system of reviewers, something like you would imagine that Google uses for ranking and rating sites. Basically they use it to try to fight "spam" like if someone just creates an account and leaves a bad review some where and does not log back into their account the review will usually fall off. Or if a company is hit with a wave of bad reviews like an attack, they will moderate them off. One that I can think of locally that comes to mind is this story http://www.wsmv.com/story/24234919/reaction-swift-after-mortons-customer-with-cancer-told-to-remove-hat It went viral on reddit and generated hundreds of bad reviews, http://www.reddit.com/r/nashville/comments/1syt3t/going_to_mortons_steakhouse_dont_wear_a_skullcap/  People even noted that Yelp started removing the reviews, http://www.reddit.com/r/nashville/comments/1syt3t/going_to_mortons_steakhouse_dont_wear_a_skullcap/ce37y4z

Yelp really is controversial in our industry, here is another good post about them http://articles.latimes.com/2013/apr/22/local/la-me--banks-yelp-backlash-20130423 and an ama from a yelp employee on reddit http://www.reddit.com/r/IAmA/comments/1vni7p/i_work_for_yelp_ama/

But about your issue, one thing I have heard, I cannot confirm myself, is that multiple reviews on the same company by a person or reviews that are out of your normal review area are hit by the filter a lot. I have seen other SEO companies complain to no avail when they have a client that is a tourist destination that gets reviews from people outside the area and they get removed.

I am sorry about the issue that you are having and that it was such an expensive issue, but that is the breadth of what I know about yelp.

This is really a decision that you need to make. It is akin to asking what kind of vehicle you should buy. If I were in your situation what I would do is write out a feature list that I want and find which platform closely integrates with it.

Also, if you are not on a hard deadline play with them all before you make a decision. Then you will know what you are getting into.