trogau

You can query core, plugin, and themes individually, or check all at once.
It defines four new methods:
<ul>
<li>xmlrpcCoreUpdateCheck – checks core, returns true/false</li>
<li>xmlrpcPluginUpdateCheck – checks plugins, returns true/false</li>
<li>xmlrpcThemeUpdateCheck – checks themes, returns true/false</li>
<li>xmlrpcUpdatesCheck – checks all of the above, returns an array of trues/falses.</li>
</ul>
The plugin was created primarily for WPUpCheck (http://trog.qgl.org/wpupcheck/), a simple 
Windows application that remotely polls a WordPress site to see if updates are available.

XML-RPC Update Check

This plugin provides XML-RPC methods for checking the update status of WordPress websites.

WordPress.org

Dion Hulse

Andrew Nacin

Most sites are able to apply updates in the background. Background Update Tester checks your site for compatibility and explains any problems.
After activating this plugin, visit the Dashboard → Update Tester screen. (If you are using multisite, visit Updates → Update Tester in the network admin.)
This is an initial release.

Background Update Tester

Most sites are able to apply updates in the background. Background Update Tester checks your site for compatibility and explains any problems.

XML-RPC Update Check vs Background Update Tester