The code itself looks OK. First, you can examine chmod's return value. Manual says that it returns the number of successfully chmod'ed files. So you can do something like:

chmod $mod, $file or die "Couldn't chmod $file";
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Then you can check if you have enough permissions to change attributes of the file. If you want to incorporate this checks into your program, then read the "perldoc -f -X".

HTH.