Trouble with this is that it doesn't make the best use of your hardware if you have machines that run at different speeds or if some data files take longer to process than others.
When I was trying to solve a similar problem (in my case, rendering individual frames of video), using whatever spare cycles were available across a whole bunch of machines (so different amounts of CPU were available on different boxes and at different times) my solution was for the individual renderers to request work units from a master, and rather than just mounting the master's filesystem and hoping for the best, they made a request to my own application. My application was a simple perl script that they accessed over telnet. The script was only working on its local filesystem so locking worked reliably, and simply told each client the filename that it should next work on. The clients then grabbed that file using NFS.
That's what I think you should do rather than randomising the list - randomising will reduce the problem, but won't eliminate it.
However, if you do want to randomise, then the wanted function should build up a list instead of doing any processing on the files. You then shuffle that list, and only after that do you process the files.