Your kernel was built with "gcc" version "4.2.3", while you are
trying to use "/usr/bin/gcc" version "4.2.4". This configuration
is not recommended and VMware Player may crash if you'll continue.
Please try to use exactly same compiler as one used for building
your kernel. Do you want to go with compiler "/usr/bin/gcc"
version "4.2.4" anyway? [no]

It didn’t take very long to find a thread about this – http://ge.ubuntuforums.com/showthread.php?t=963825.  I took the suggest of some of the users here and chose YES.  SNAPSHOT YOUR MACHINES BEFORE YOU TRY SOMETHING UNPROVEN!

Well now it complained that it couldnt locate the Linux C Header files:

The header files in /usr/include are generally for C libraries, not for the
running kernel. If you do not have kernel header files in your /usr/src
directory, you probably do not have the kernel-source package installed. Are yousure that /usr/include contains the header files associated with your running
kernel? [no]

Weird.  So now I had to manually install the Linux Headers.  I did this by issuing:

apt-get install linux-headers-`uname -r` build-essential

I now re-ran perl /usr/src/vmware-tools-distrib/vmware-install.pl.  I again of course had to tell the installer to continue compiling using gcc 4.2.4, but now it didnt complain about the C headers. The install completed successfully.