"Reviews From Around The Web" aren't showing up on my client's Google+ Local / Places Page

This is likely due to profile authority left by the reviewers on each of those sites. Additionally, Google does not show all reviews from all of these sites, they'd prefer to show their own.

Profile authority is a critical component to understand when dealing with reviews, and this has become a much bigger factor since Hummingbird.

Reviews are likely not the cause for his lack of rankings thought. Review quantity (and even quality) are not a major factor in ranking, but they play a big role in the service area.

Also, let's not talk about the top 7, unless he's 1-3, he's not in the game.

While reviews are the third of three important pillars in ranking for local, Profiles and Citations take the weight to at least get on the map.

Make sure you're following profile best practices, have a score above 60% on Getlisted.org and have enough media with it properly socially propagated in their profiles.

Even if it's one a month, you need quality local citations. The local chamber is a quick and easy way. It it's a chiropractor you're dealing with, think partners like a massage therapist. Their website is your best citation, make sure you follow all the best practices for on the site optimization.

As far as reviews, consider a review acquisition strategy. You don't want to violate the T&C's of the site, but encouraging satisfied customers on Google is lucrative.