If I understand what you're asking, you want to detect gaps in the sequence if you've only skipped one number; you don't care about gaps of 2 or more, like the one between 0005 and 9996.

So for each number you know exists (call it 'n'), if n+2 (with "wraparound" after 9999 back to 0001) exists but n+1 does not, that's a "skip":

my @skips = get_skips(qw(9996 9998 9999 0001 0003 0005));

print join(',', sort @skips) . "\n"; # 0002,0004,9997

sub next_seq {
    my $n = shift() + 1;
    if ($n > 9999) {
        $n = 1;
    }
    return sprintf '%04d', $n;
}

sub get_skips {
    my %s = map { $_, 1 } @_;
    my @r;
    for (keys %s) {
        my $next = next_seq($_);
        my $nextnext = next_seq($next);
        if (exists($s{$nextnext}) && ! exists($s{$next})) {
            push @r, $next;
        }
    }
    return @r;
}
[download]

I'll leave extracting the list of numbers from the filenames to you.