What is installer.failurerequests in the root directory?

It's safe to delete this file.

It is a file left behind by the OS X installer in later versions. It seems to always be there after installation, so its existence does not indicate a failure in it self.

What the installer actually uses the file for is not known to me. It might be used if the installer fails/crashes, to indicate what the installer was doing at the time of the crash - but this is guesswork.