Hi Adrian
I would take a look at your backlink profile / rankings via the following tools:
Google Webmaster Tools
Majestic
SEMRush
I would assess your anchor texts, the topical relevance of your backlinks, age of your links, and also your backlinks individual metrics. Not only for your own backlinks, but your competitors as well based on keywords/queries you want to rank for.
Also, take a look at Moz's On-Page Grader and see if there are any opportunities you may be missing out on.
From there, I would also look into Schema.org - they offer keyword markup opportunities that can help you better assist crawlers in understanding the topics/meanings of a particular page. Also - take a look at their medical markup opportunities as well.
Lastly, for the time being, if you have a lot of traffic coming to the homepage for these keywords and queries, take a look at A/B testing your homepage to get users to those internal pages more quickly. You have quite a bit of navigation going on and your rotating banner is quite large and confusing, especially when you click the arrows. I see images, but then I click on one that I think is taking me to whitening, but then I am taken to dental warning signs.
Consider this area your opportunity to grab users attentions, get them to where they were searching for, and utilize internal linking in a more effect manner.
You can use the following tools if you want to test:
Visual Website Optimizer (GREAT resource section)
Google Experiments
Optimizely
Also, check your robots.txt/meta robots and sitemap (and check that it's submitted to Google and Bing Webmaster Tools) to make sure everything is being properly indexed and crawled.
Just some things to think about - hope this helps! Good luck!