Like WordPress states on their WordPress 3.2 pre-release page client’s hosts need to be using MySQL 5 and at least PHP 5.2.4. There’s a plugin called Health Check that will let you know either way. I’d hurry and install this plugin because if the environment is not OK you’re going to have to login to the client’s cpanel and see if you can upgrade both or if you have to contact their host and ask them to make this an option.
Oh I forgot to say whether replacing WordPress jQuery 1.6.1 with jQuery 1.4.4 causes anything to break. I’ve tested the Widgets and Menus manager and everything works as expected.