In general, BPS only checks if XCache, eAccelerator or other extensions are loaded and does not actually use these extensions in any way. Most likely the php errors are being caused by a caching plugin that you have installed. It could be that BPS is related to the problem with the caching plugin if BPS is doing something that is causing the caching plugin to malfunction. Are you using a caching plugin? If so, which caching plugin are you using?
We are aware of 1 problem with W3TC that will be corrected in the next BPS release. The security filter in the Forum link below in the BPS root .htaccess file causes W3TC minify relative URL paths to be blocked.
http://forum.ait-pro.com/forums/topic/w3tc-minify-problem/#post-11046
Do you see any errors in your BPS Security Log that are related to this issue? If so, post the error. Please only post up to 5 errors from your Security Log and not your entire Security Log file. Thank you.