I found the cause of the error regarding the REST API. I assume the WebApp suffers from the same issue.
Situation:
WebLogic 12R2 is shipping Jersey 2 and Jackson 2.4.3.
Also since version 2, Jersey is shipping Moxy as the default JSON processor.
Solution:
I wrote an weblogic.xml, which makes our Jackson classes available to the correct classloader. I also edited the web.xml to disable Moxy as default JSON processor for Jersey, so it uses our Jackson instead.
I was able to pin it down to classloading, trying a solution right now.