my @flattened_array = flatten($nested_array_ref);

sub flatten {

    my $array = shift;
    my @results = ();

    foreach my $element ( @$array ) {

        if( ref $element eq 'ARRAY' ) {
            push @results, flatten($element);
        }
        elsif( $element ) {
            push @results, $element;
        }
    }

    return @results;
}
[download]

update: I investigated per rob_au's concerns with the following code using the above subroutine:

use Data::Dumper;
use strict;

my $nested_array_ref = [
    '',
    [
        'a',
        [
            'b',
            'c'
        ],
        '',
        'd'
    ],
    'value'
];

my @flattened_array = flatten($nested_array_ref);

print Dumper(\@flattened_array);
[download]

and my output was this:

$VAR1 = [
          'a',
          'b',
          'c',
          'd',
          'value'
        ];
[download]

the example i gave explicitly passed an array_ref into the function to begin with, and @results is local to the subroutine, and does not get blown away during recursion.