That's a lot of code.

Well, as for suggestions, use perltidy. Hopefully you see why.

    if (!defined $match) {
        print "$ip: ERROR_1\n";
        print LOG "$ip: ERROR_1\n";
        return;
    }
...
    if (!defined $match) {
        print "$ip: ERROR_13\n";
        print LOG "$ip: ERROR_13\n";
        return;    
        }
...
sub get_inventory {
    my ($ip, $t) = (@_);
    if (!$t->cmd('terminal length 0')) {
        print "$ip: Error changing terminal length\n";
        print LOG "$ip: Error changing terminal length\n";
        }
        my @show_run = $t->cmd('show run | inc hostname');
        ...
[download]

Did you assemble this stuff from different sources?