Speaking of vias in pads, here's a reason we're not terribly fond of the technique of using solder mask to tent the bottom side of a via in a BGA pad.
As I mentioned in my last post, capping the bottom of the via with soldermask is sometimes an acceptable method for dealing with a via in pad. It's not a desirable method, but it does sometimes work. However, with BGAs, the top-open via can still wick solder down to fill the space. At the very least, you will end up with a hefty void in the BGA solder ball. At worst, you will end up with an open, as illustrated here.
Best option: Fill and plate over the via.
Does cheap mass production = this perfect day?