Take a look at this forum post. Here's what a mod had to say (in response to the question):
I'm currently using my HTC Wildfire S power adapter (TC E250 charger
(5V/1A)), to power Raspberry - while it is working for basic setup,
I'm afraid it may not be powerful enough while turbo over-clocking is
enabled, resulting in SD card corruption (my raspberry stopped working
"just like that" a week ago - SD card was corrupted, card itself is
fine as far as I can tell - so I suspect the over-clocking was the
reason). Question is - is there any power supply out there that will
give raspberry enough juice even when it is over-clocked?
I don't think the power supply is relevant. Overclocked or not, the
power consumption change is negligible, the actual SD card has much
more to do with it. If your tp1-tp2 voltage is near enough 5V, you can
almost rule out the supply (though there are some cases where you get
5v, but with a large ripple). I have some cards that run great with
the pi overclocked, while others refuse to boot properly. I am yet to
experience sd card corruption, but that's probably because of the
cards I use, not anything else.
Basically what it's saying is that your SD card is at fault, not your power supply (which you said was outputting 5V, and because it is a smartphone charger I am assuming that is at 1000 mA).