Gotta validate the inputted word by checking that it indeed consists of the chars in $random_string.

Perhaps I'm misunderstanding you, but this sounds like you want to validate that the two sets of string characters are equal (the 'compare uniquely')--not that the two strings are equal. If this is the case, the following is an option:

use strict;
use warnings;

my $word          = 'FHDJSKAL';
my $random_string = 'ALSKDJFH';

if ([sort ("\U$word" =~ /./g)] ~~ [sort ("\U$random_string" =~ /./g)])
+ {
    print "Good word.\n";
}
else {
    print "Try again.\n";
    print "\n";
}
[download]

Hope this helps!

Update: Replaced the hash solution with one using the smart operator (~~), as the former didn't match properly.