The versions of jQuery and jQuery UI in use are vulnerable to several issues

Similar to JRASERVER-43422, the version of jQuery used (currently version 1.10.2) is vulnerable to jQuery issue 2432 (3rd party $.get() auto executes if content type is text/javascript) and 11974 (parseHTML executes inline scripts like event handlers). Additionally, the version of jQuery UI in use (1.8.24) is vulnerable to CVE-2010-5312 and an attacker can exploit this issue if they are able to provide values to "title" of a jQuery ui dialogue. Actual exploitation / impact to Bamboo depends upon if & how the vulnerable code paths are used.

On a related note, http://research.insecurelabs.org/jquery/test/ can be used to check jQuery versions for issues.