Apart from the syntax problem, MySQL versions earlier than 4.1 (which is far from stable at the moment) do not support subqueries.

Here's a workaround to such limitation.

#!/usr/bin/perl -w
use strict;
use DBI;

my ($dbh, $rows);

$dbh = DBI->connect('dbi:mysql:test', 
    'myusername',
    'mypassword',
    {RaiseError=>1}) ||
   die "Error opening database: $DBI::errstr\n";

#
# First, get destination from your table
#
my ($destination) = @{$dbh->selectcol_arrayref(qq{
     SELECT destination
     FROM checkin
     WHERE firstname='Henry' AND lastname='Rollins'}
     )} 
#    || die "destination not found\n"; # wrong 
     or die "destination not found\n"; # correct
#
# Notice that the script fails if destination is not found.
# 

# 
# then, use $destination to update the table
#
$rows = $dbh->do(qq{UPDATE checkin
        SET    destination = '$destination'
        WHERE  firstname='Bill' AND lastname='Gates'})
        || die "Couldn't update record : $DBI::errstr";

print "$rows row(s) updated in checkin";
$dbh->disconnect || die "Failed to disconnect\n";
[download]

A few comments:

• You are using UPDATE and then printing "rows added."
  Be aware that the UPDATE statement modifies an existing record. It does not add rows.
• What you are doing with your SQL statements is taking one column (destination) from a row identified by name and surname, and then inserting such column into another record identified by another name/surname pair.
  Make sure that this is really what you want to do.
• You are using a MySQL installation with "root" user and no password.
  This is a huge security risk. Please fix it as fast as you can.

update - Fixed a small bug in the script.

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[download]