It's perfectly clear how mobile device use has changed the way websites are configured, and earning the "mobile-friendly" tag on Google search results is exceedingly important.
Reviewing a website to bring it up-to-speed with current responsive design best practices can be a headache as the page count increases. Mercifully, Google has provided a review tool to make a site rerelease a lot less painless.
Start with Google Webmaster Tools
Google Webmaster Tools takes a few minutes to setup and verify for a certain website, and you'll most likely need to wait for Google to finish crawling and indexing every page on the domain.
Once this process is finished, navigate to "Mobile Usability" under "Search Traffic" to get a complete rundown of usability errors contained in the current web design and coding:
Touch Elements Too Close
Navigation elements and buttons are too small and close together for touch devices. This is most common in text menus that are better off as accordion menus.
Small Font Size
Often found in product descriptions or image descriptions. Requires experimentation and testing to find the right fit for your website.
Viewport Not Configured
The view window is not scaling to the sizes found in the myriad of web devices. Easily the most annoying incompatibility for mobile users, but simple to fix.
Content Not Sized to Viewport
Content needs to reposition to avoid any side-scrolling to view content. Takes more time to consider ideal repositioning, but well worth the effort.
Flash Usage
Mostly incompatible with mobile devices.