We'd been told to open appliances when they arrive, and look for damage. Sure enough, we found a big dent on the range.
Exhibits A and B:
First, we called the store (which connected us to a call center) and were offered a couple measily options (10% off our next purchase... what "next" purchase?). Next, we headed to the store, ready to haggle and show photo-evidence of the damage.
The store employee started talking about replacing the appliance, but I said I'd be happy with a partial refund. He seemed relieved and refunded us about 18% of the purchase price (which was already on a post-holiday sale)! WIN!