I imagine that plenty of eyes have combed through the reference client's source code. But the code is still changing for a variety of reasons (features, patches, improvements, etc).
I didn't find that much information regarding security audits other than this post that says the Bitcoin Foundation hired Sergio Demian Lerner as a core security auditor.
As Core Security Auditor, Sergio will be dedicated to the ongoing security review of changes to the core code. Sergio has been volunteering his time and expertise since March 2012 and over the last couple of years, he has found, reported, and helped fix several vulnerabilities in the core code. Sergio has been an independent security researcher and consultant since 2011 and will continue to work with his other clients in addition to his role at the foundation.
Are security audits, whether internal or external, performed on the source code of Bitcoin Core? If so, by whom and how often?