Sometimes it's very helpful to write a small example (as you have done in your OP) and see the result. Data::Dumper and Data::Dump are very useful for this.

>perl -wMstrict -le
"use Data::Dumper;
 ;;
 my %hash;
 ;;
 push @{ $hash{'one'} }, qw(fee fie foe fum), undef, 'oops';
 print Dumper \%hash;
 ;;
 my $defined_pushed = grep defined, @{ $hash{'one'} };
 print $defined_pushed;
"
$VAR1 = {
          'one' => [
                     'fee',
                     'fie',
                     'foe',
                     'fum',
                     undef,
                     'oops'
                   ]
        };

5
[download]

See also Basic debugging checklist.