That's such tightly constrained input that only the first value of a row is needed to check it.

sub are_consecutive {
    my $i = $_[0];
    $_ == $i++ or return 0 for @_;
    1;
}

are_consecutive(@{$_}) or die "User can't count.$/" for values %hsh;

my @big = sort {$a <=> $b} map {@{$_}} values %hsh;
$big[0] == 0 && are_consecutive(@big) or die "Bad big.$/";
# originally had soln in terms of $big[0] == 0 and $big[-1] == $#big
# rejected because equal number of missing and doubled terms not detec
+ted
[download]

The usual hash for checking uniqueness is unneeded here because of the additional arithmetic properties you want.

What application requires that a user partition 0..N this way?

Update: cleaned up and corrected for offsetting double errors

After Compline,
Zaxo