But in the next line in the actionscript code after the external interface call, if I inspect the value of paragraphStyleStr, it is null.
Have you checked for an error via a try catch statement or is the result null? There's a try catch example here where you could catch an error or security error message:
http://help.adobe.com/en_US/FlashPlatform/reference/actionscript/3/flash/external/External Interface.html#callhttp://help.adobe.com/en_US/FlashPlatform/reference/actionscript/3/flash/external/External Interface.html#call%28%29
If there's no error have you tried casting
var paragraphStyleStr:String = String(ExternalInterface.call("getParagraphStyles"));
I do have a try / catch surrounding the call. I had not thought of trying an explicit cast to String. I tried it and it is throwing an Undefined error on the variable.
I've posted the question in the InDesign Scripting Forum per suggestion. I did just notice that the InDesign CC SDK is not officially released yet. Perhaps the interface mechanism I am using isn't fully gelled yet in InDesign CC.
Thanks all for the replies and suggestions. Something odd is going on with this it seems ...
What FlashBuilder SDK are you using. I've had lots of problems moving older FB4.5/FlashCS6 projects over to FB4.7. By default FB4.7 forces you into the new AIR 3.4 SDK. Dropping back to the Flex 4.6 SDK solved most of my problems with older projects.