Latest W3TC. Current on version of New Relic, Running my CloudFlare through the W3TC plugin.
System is a EC2 Micro, with Nginx. Opcode is in use an up to date, as is the 5.4 fastcgi version of PHP.
Every transaction gets me one of these:
Declaration of W3_Cache_Apc::delete() should be compatible with W3_Cache_Base::delete($key, $group = '')
That is from my New Relic log, where I of course have a "fail" rate of 100% because of it.
Turning off plugins does not help. No more than half a dozen lines of custom code. Adding templates and hookable functions to a cruddy theme that did not come with them. Should be way out of your territory I would think.
Errors go to 0 when W3TC is disabled, after you give it a chance to replace the file in the root of content... which makes me think that I should bring up that one of your master files was found half written out yesterday and had to be replaced with a backup. It was the one in the root or cache folder, I can't remember exactly where it came from.
Config file available on request.