How is this _PHP_ bug? Since all that changed is mysql version (to a _release candidate_!) I find it funny you report this here..

Table and constraint creation are ok with cli mysql client.
Table and constraint creation are ok with phpmyadmin with mysql php's extension (i known that mysql php's extension has not multi_query() equivalent method).
Removing "alter table... add constraint" from sql in php script resolve the problem.
Execute several queries on mysql 5.1 RC server with mysqli::multi_queries() without any "alter table... add constraint" is ok.
In conclusion, All work fine between this mysql 5.1 RC version and php's mysqli extension, except this.
So, I think that it must be interesting to check mysqli php's extension compatibility with mysql 5.1, even if mysql version is a RC.

 Hi,
I have tried both 5.2.7RC4 and 5.3-dev (with libmysql and mysqlnd) and can reproduce the problem. I have tracked the C/S traffic and there is an error in the middle of the multi-statement, which cancels the whole statement. I have added two var_dumps() to your example, like :

$sql = 'SET SQL_MODE=NO_AUTO_VALUE_ON_ZERO; DROP TABLE IF EXISTS `bank_transactions`; CREATE TABLE `bank_transactions` ( `id` int(10) unsigned NOT NULL AUTO_INCREMENT, `client_id` int(10) unsigned NOT NULL, PRIMARY KEY (`id`), KEY `client` (`client_id`)) ENGINE=InnoDB  DEFAULT CHARSET=utf8 ROW_FORMAT=DYNAMIC; DROP TABLE IF EXISTS `clients`; CREATE TABLE `clients` ( `id` int(10) unsigned NOT NULL AUTO_INCREMENT, PRIMARY KEY (`id`)) ENGINE=InnoDB  DEFAULT CHARSET=utf8 ROW_FORMAT=DYNAMIC; ALTER TABLE `bank_transactions` ADD CONSTRAINT `bank_transactions_ibfk_1` FOREIGN KEY (`client_id`) REFERENCES `clients` (`id`) ON UPDATE CASCADE';

$mysqli = new mysqli('127.0.0.1', 'root', 'root', 'db');

if ($mysqli->connect_error) {
    printf('Connect failed: %s\n', mysqli_connect_error());
} else {
	if (!$mysqli->multi_query($sql)) {
		printf('Unable to execute sql');
	} else {
		do {
			if ($result = $mysqli->store_result()) {
				var_dump($result);
				$result->free();
			} else {
				var_dump(mysqli_error($mysqli));
			}
		} while ($mysqli->next_result());
		var_dump(mysqli_error($mysqli));
	}

	$mysqli->close();
}

and the output is :
andrey@winnie:~/dev/tmp/php5.2-200811191530$ ./php ../../vanilla/php5_3/a.php
string(0) ""
string(0) ""
string(54) "Can't create table 'db.bank_transactions' (errno: 150)"
andrey@winnie:~/dev/tmp/php5.2-200811191530$ ./php -v
PHP 5.2.7RC4-dev (cli) (built: Nov 19 2008 18:49:58)
Copyright (c) 1997-2008 The PHP Group
Zend Engine v2.2.0, Copyright (c) 1998-2008 Zend Technologies

andrey@winnie:~/dev/tmp/php5.2-200811191530$ /work/mysql-server/mysql-5.1-binprot/extra/perror 150
MySQL error code 150: Foreign key constraint is incorrectly formed

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So I don't know why from the CLI the problem doesn't happen, it needs further analyse to see why the environment is different. Also probably needs a test case in C using libmysql, which will probably exhibit the same problems.

A MySQL server bug 
http://bugs.mysql.com/bug.php?id=40877

Sorry to close it as bogus, it's not client related, thus not mysqli.