What are some breakthrough marketing strategies to grow and scale a local business?

Great question - local marketing is absolutely essential nowadays. Especially as few people are navigating social media looking for tooth whitening services, these will become more profitable than online over time.

Here's a quick list of tools I suggest using to bolster your current social media work.
1 - Set up Google My Business account and get it address-verified (they mail you a code)
2 - Key words - ensure city/ town / suburb / state or county are all included in meta data
3 - Directory listings - Get yourself listed on free and paid sites. If you can afford a small spend www.brightlocal.com is worthwhile
4 - Use Facebook local targeting for advertising / brand building
5 - Set up Google Alerts for key phrases in the news that could allow you to comment / contact / build a mailing list
6 - Join the local Business Associations and contact all the relevant local business members
7 - Go to Networking events (BNI, Chamber of Commerce, Meetup.com, Eventbrite)
8 - get happy customers to write Testimonials on Google My Business, Also reproduce them on your website
9 - Use media relations to get articles in local newspaper, local radio, local newsletters, (check out Yahoo Groups for local lists)
10 - Ask for Referrals - by sending two business cards with your invoice
11 - Make specific requests for social sharing via your accounts
12 - Surprise and delight the customer - e.g. pay it forward - you pay to have your teeth whitened and I give a free treatment each month to a deserving individual and use that for publicity.

I hope that gives you a load of great ideas to be getting on with. But if you'd like specific coaching on what to do for this client - get in touch. You can buy 30 minutes of my time and I'll add to this.

Sttop thinking about advertising products (Google, Facebook, etc.) and focus instead on the following sequence of questions:

1. Who are my most profitable market segments? Go through your existing customers and look for things in common with respect to profitability of clients, this will give you the best bang for your buck if you can target those people. If you're targeting the wrong people none of the rest matters.

2. Where do you find them in the greatest concentration? Pay attention to where you can find these people, who else do they buy from (possible joint ventures or host beneficiary relationships), what do they read or watch, are there lists of these people, who do they look to as authorities, etc.? The more concentrated you find the the lower your costs will be since in effect you're paying per impression.

3. How do they buy? You want to mirror their buying process so if they go online and do a search for a particular keyword to make a decision you want to rank for that keyword. Maybe they are looking for certain characteristics when buying so you want to match those characteristics. Maybe they trust a certain authority so you want to be in with that authority. Or maybe they look to friends so you want to create social awareness.

These will give you information about places to look (newspapers, magazines, Yelp (it's free to list yourself so you should be on there for local marketing), online directories, review sites, maybe in the media, maybe appealing to various micro niches such as body builders or models or wedding parties. The key is to filter through those 3 questions to maximize your ROI and effectiveness.

I think you are already doing enough for the nature of business you are in. What you might need is a digital social expert to run some analytics on what you have already done to help you understand what is working and what is not, and maybe fine tune your spends.
Without knowing your competitive space it is impossible to recommend a clear communication strategy that will deliver the growth you aspire for.
Commenting generally, once you have generated enough trial, further business growth will be dependent on the quality of service you provide - right from the look and feel of your outlet / clinic, your location, parking, to the quality of dental experts and their service and customer orientation.
The very nature of your business is such that word-of-mouth is the best marketing which you can influence through your service but cannot control totally. Though a small social media nudge can help. After initial trial it is as slow build, unless you either increase locations or buy out competitors.