I'm still a firm believer that NAP audit and correction services are primarily hyped as far as their actual effect on rankings. No one gets paper phone books anymore and there's no reason to buy advertising from the likes of Yellowpages, Superpages, etc, so they are desperate to create new revenue streams. Hence when you submit your business on all these sites they automatically show you a list of even more obscure sites you are not on or your NAP doesn't match. Our best performing location has two different NAPs out there about a mile from each other. One was an old mailing address. It's 3-pack 99% of the time for all our target keywords. My determination is that what makes the difference is that the business is listed with one of the main three databases Axciom, Localese, Infogroup. Paying attention to NAP in all the second and third tier directories using a paid service is a complete waste of time and money in my opinion. I've scoured the Internet for any sort of well done study to prove the effect on rankings of NAP consistency. They can't be done as there are too many other ranking factors anyone I've found to publish any sort of article on the subject is in the industry that sells those services. You think you moved the needle making your NAPs more consistent, but most likely the timing was just coincidental. I know I sound jaded, but I've just been around the block too many times and see the money making schemes from a mile away. If you got time and money to waste, it definitely can only help if at all. If you NAP error is in another city or something, then obviously you'll have conversion issues. I'm talking about missing suite number on some or Street versus St. That kind of stuff. But I've gone off on a tangent sort of, sorry.
Here's an interesting tidbit I recently noticed. Words in the reviews are a ranking factor believe it or not. You will notice on Google 3-pack, sometimes you will see an excerpt of a review with one of your search keywords highlighted. I threw in an obscure word into a search test once where we should never come up in the 3-pack for and we did because the word was in one of our user's reviews. Very interesting.
I also think Google likes schema markup and makes much more of a difference than NAP consistency every will.