What design testing can I do before fabbing a PCB?
If the unspecified circuit is analogue or digital logic then using a simulator is a definite thing to do. There are quite a few free simulators around and LTSpice springs to mind. It's a relatively steep learning curve but totally worth the effort. 

If it's a micro based design then I can't offer help other than to suggest you double check every pin. If it's an EPLD, then double check the pins and run simulations of the logic within the suite of tools usually provided by the vendors.