Here's some insider info, guys - take it or leave it.
The issue is a hardware one (in short - Mini is too small for modern components, and some hacky solutions had to be applied), and it's much more pronounced on lock screen due to protection against butt dials. The flaw was discovered at later stages of production, so the cutout in official silicone case is not a whimsical decision. Apple is preparing a statement currently, and the course of actions is most likely a recall of big batch of Minis. There is a chance they may try to do it in a similar way to iPhone 4 - I don't know the details of this solution, but if they go this way it'd most likely be a case with some conductive parts per customer. I've also heard about probably trying to goad users into not using screen protectors, but that is already well into rumors territory.