Found while reviewing patch for bug 10387.
The AJAX callback code in skins/common/ajax.js attempts to call index.php directly:
uri = wgServer + wgScriptPath + "/index.php?action=ajax";
On a system where index.php doesn't work, this doesn't get us anywhere. The system needs to pass $wgScript as well as $wgScriptPath, then the AJAX code should use that instead of hardcoding index.php.