Few more things, we are quite sure that if you work using the wallet UI you won't be able to break anything, however even if you are not a coder it would help a lot if you try the system as a user if only to generate good test data and provide feedback about the user interface.
It would be great if you can run your own testnet node. Feel free to shuffle using more than one account and more than one node at the same time. You can even try with the same account on different nodes, the blockchain should be able to handle these cases.
If you need testnxt post here.
We suspect that to really break things you'll need to review the source code and submit transactions manually (i.e. not rely on the default shuffler, perhaps try to create an evil shuffler)
To start with, checkout the 1.7.4 source code available here
https://bitbucket.org/JeanLucPicard/nxt/src , I recommend that you focus on the Shuffling*.java and Shuffler.java sources under the java/nxt folder. One thing we sometimes get wrong is the validateAttachment methods in ShufflingTransaction.java, if you find something there that's a low hanging fruit.
The main algorithm is implemented in the Shuffling.process() method and the source code for blaming a cheater is in the blame() method.
In my view, if you are able to break things really badly and explain what you did we can probably provide a larger bounty.