CNET just posted a breakdown of the Mini costs:
$188 to build the mini.
The custom-sized screen is the biggest cost: $80 and the biggest bottleneck for ramping up production. The screens come from LG and AUO, with AUO being the weak link in the supply chain.
Going by past Apple pricing it appears that at $329 Apple did, in fact, drop the price before launch. A $188 build cost would normally mean a $350 price in iOS land.