The blockchain is currently about 15GB, and grows every time there's a transaction. That's a problem. Most phones don't have 15GB of free space. You'd have to get an SD card, just to hold it and that is only a temporary solution, since it'll keep growing.
Also this would be a real problem if BTC was actually used like a major currency and not just played with by speculators as the number of transactions would be orders of magnitude higher, and thus so would the growth.
So it would be totally unrealistic to just store it on mobile devices, which is something you'd probably want to do if you were going to use it as a general purpose kind of payment system, security issues aside and those are not minor.