I tried to start a process instance via the rest api that has a single script task and got a 500 response with "can't find scripting engine for groovy. I noticed that the groovy jar is not included in the lib folder for the activiti-rest war. Copying the groovy jar from activiti-explorer fixes the issue.
The groovy-jar is optional and only needed if you use groovy, as with any 3rd party lib you would use yourself. Since the REST does not depend on that, it's not set as a dependency on the rest-webapp. This is not a bug, it's intentional…