Reading the comments here, I'm surprised at how broadly the terrible situation in the Congo is being generalized. This is not one immorally-sourced component among many, it's a massive outlier: A rare element with its richest mineral source in one of the poorest, most chaotic and war-torn nations on the planet.
It's correspondingly an incredibly hard problem to solve. At an extreme, Apple probably has the cash to buy its own mines for cobalt but how can they ensure that their suppliers use it exclusively? It's a fungible commodity, after all.
If anyone has any ideas that don't revolve around armed 'humanitarian' intervention in the DRC, I'd love to hear them.
Also, I'd be interested to hear what problem #2 is if this one could be eliminated. My suspicion is that its degree of horribleness would be a significant drop-off.