The updating instructions for version 1.6.3 say:

The index.php file has been updated for Version 1.6.3, so you will need to overwrite your existing index.php file with the new file from Version 1.6.3.

Can anyone tell me to which index.php file this refers?  the one in the system folder?

Thanks,
Jules

No, the one in the root folder. You know:

That one

For those of us that are running the MSM and followed these directions, does the update also require that we update the index.php in each subdirectory on our server (one per site in the MSM)?

/public_html
-index.php
-path.php
/site2
  -index.php <- does this need to be updated too?
  -path.php
/site3
  -index.php <- does this need to be updated too?
  -path.php

If the index.php actually did change (which does not happen often), yes, you should replace the index.php in the subdirectory as well. It is a copy of the index.php in the root directory, and changes when that file does.