If you take a lazy approach to optimizing for mobile traffic, where you automatically redirect anyone who visits your site from a mobile device to the homepage, rather than the page they clicked, you will definitely want to rethink their strategy and correct it.
Google has announced a change where they will take into account a website's behavior toward mobile users. If Google believes your site will redirect a mobile visitor to your homepage, instead of the internal page that showed in the search results, Google will clearly note this directly in the search results, saying "May open the site's homepage" with an option below it to "Try anyway."
Many mobile users find it quite aggravating when they try to find internal page, click through on a search result that appears to be going to that internal page, and end up being redirected to the homepage, as it can often be difficult to find that internal page from the homepage.
Many users who get redirected like this tend to return to the search results when this happens, which alerts Google to the fact that searchers aren't happy with what they found when they clicked through. Google prefers to send people to sites that provide a good user experience, as it keeps users from switching to another search engine.
If you aren't sure of exactly how your website handles mobile traffic, you can utilize a few different Google tools to ensure you serve your Google traffic properly.
Your first stop should be Google Webmaster Tools, which includes a section called "Faulty Redirects" to show when you aren't handling your mobile traffic properly. It is found in the Smartphone Crawl Errors section under URL errors. You can then click on any of the faulty redirects to find out the pages and the problems associated with it.
You can also use a Chrome extension and do Google searches yourself to see what happens when you click through from the Google search result to your page. Don't forget to do searches that will bring up internal pages to the site, since it is the internal page handling that Google will show alerts for in the search results.
Google also reminds users that responsive design is effective for websites, as it will serve the same content to both desktop and mobile users, while presenting it in a format that each type can easily read and use.