We need a sample of the data since there are conditions on which we will not be checking diff's. However I would suggest something like the following.

#!/perl

use strict;
use warnings;

my @months = qw(January February March April May June July 
                August September October November December);

open(FIRST,  "<first.file")  or die "$!";
open(SECOND, "<second.file") or die "$!";

#if the files aren't huge you can slurp and comapre arrays

my @first  = <FIRST>;
my @second = <SECOND>;

close(FIRST);
close(SECOND);

open(DIFF, ">diff.file) or die "$!";

for(my $i = 0; $i < $#first; $i++)
{
     my $is_date = 0;
     foreach(@months)
     {
          if($first[$i] =~ m{$_\s*\d{1,2}})
          { 
             $is_date = 1;
             last;
          }
     }

     if(!$is_date)
     {
        if($first[$i] ne $second[$i])
        {
             print DIFF, "Difference found @ line: ".$i."\n";
             print DIFF, "File 1: ".$first[$i]."\n";
             print DIFF, "File 2: ".$second[$i]."\n";
             print DIFF, "----------------------------\n";
        }
     }
}
close(DIFF);
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