1 #!/usr/bin/perl -w

You should use the strict pragma as well:

        use strict;

      3 #open file
      4 open(OUTFILE, ">/media/hda3/differences.txt") or die("Unable t
+o open file");
      5 
      6 #read file into array
      7 @data = <FILE>;  

The filehandle FILE has not been opened yet so @data will be filled wi
+th nothing;

      9 #close file

All of the comments up to now have been superfluous.

     10 close (FILE);
     11 
     12 #Used to test if data is read into array
     13 #print $data[2];                                      

How is that supposed to "test if data is read into array"?

     15 #open file to save differences
     16 open(FILE, "/media/hda3/differences.txt");

You are opening the file too late to be able read it on line 7.  You s
+hould *always* verify that the file opened correctly:

        open FILE, '<', '/media/hda3/differences.txt' or die "Cannot o
+pen '/media/hda3/differences.txt' $!";

     18 #loop to determine differences
     19 for ($i=0; $i<377; $i++)
     20   {
     21   for($j=$i+1; $j<377; $j++)
     22      {

Why 377?  Why not just use the actual size of the array:

        for my $i ( 0 .. $#data ) {
          for my $j ( $i + 1 .. $#data ) {

     23      $command_line = "cmp -l /media/hda3/2967test/" $data[$i] 
+" /media/hda3/2967test/" $data[$j] "| wc -l";

There should be operators between the strings and the variables:

             $command_line = "cmp -l /media/hda3/2967test/" . $data[ $
+i ] . " /media/hda3/2967test/" . $data[ $j ] . " | wc -l";

Or just use string interpolation:

             $command_line = "cmp -l /media/hda3/2967test/$data[$i] /m
+edia/hda3/2967test/$data[$j] | wc -l";

     24      $diff_count = system $command_line;

system does not return what you seem to think it returns.  You probabl
+y want something like:

             my $command_line = "cmp -l /media/hda3/2967test/$data[$i]
+ /media/hda3/2967test/$data[$j]";

             my $diff_count = () = `$command_line`;

     25      print OUTFILE ($data[$i], "\t", $date[$j], "\t", $diff_co
+unt, "\n");

The strict pragma would have caught your typo, there is no @date array
+ defined.

     26      }   
     27   }
     28 
     29 #close file
     30 close(FILE);
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