[sgornick]

Bitcoin payments for person-to-person can be done on mobile. Merchants can run their own point-of-sale or use a hosted solution (or, us a mobile / tablet, just like an individual).

For merchants, just like if VISA/Mastercard/Debit card, etc., goes out due to power problems (and there there is no battery backup or local generation), a merchant can't accept payments until power is restored.

As far as power outages for those mining -- there is no disturbance to Bitcoin even for lots of power distruptions. If the entire world goes dark, your inability to spend bitcoins will be the least of your problems.