Ok. first let me try and understand your problem.
You are trying to create a new entry using the java API and you are getting this error.
1. Are you trying to populate the field with field ID 112? If so, with what value? As far as I remember, field ID 112 is a reserved ID for a group name. So, make sure that you are not populating it with just any random string or number.
2. I didnt quite understand this part - "I'm trying to set a field ID on the new case (I'm not setting field ID 112 if that helps) to a specific value which has not been configured in a drop down list or similar. "
does that mean that you are trying to populate the field which has a drop down, but you have not filled any values in the drop down before creating entry using API?
Thanks,
Anuj.