When I publish my web application and have
Precompile during publishing
Unable to load DLL 'VSPerf110.dll': The specified module could not be
found. (Exception from HRESULT: 0x8007007E)
OK it sounds like this application is trying to make use of the Profiler API on the production server. There may be some performance tracking Profile code in this application that may need to be commented out or removed.
Per this MSDN documentation on the Profileer API for VS 2012, "Your build must reference the Microsoft.VisualStudio.Profiler.dll library, located in the Microsoft Visual Studio 9\Team Tools\Performance Tools directory."