The anonymity that every mainstream article claims Bitcoin has is not nearly as strong as it's made out to be[1][2][3].
The built-in deflationary aspect of Bitcoin seems to prevent it from being used as a "serious" currency. Hiding money under your mattress should never be the optimal approach to making more money. (It might not prevent people from using the currency, but it's highly sub-optimal.)
The fragility of the currency concerns me (by which I mean the way it's possible to lose massive amounts of money by losing a file or forgetting a password). Maybe this is a technical problem that will be solved with a more mature ecosystem, but I like the way that a real bank always has ways to access money when bad things happen (at least in a functioning banking system). This thread[4] documents the loss of about 70,000 Bitcoins, which is worth about ten million dollars today. Related to this, if somebody hacked the EFF's Twitter account and posted that they were accepting Bitcoin donations on some address, a lot of Bitcoins would disappear into somebodies wallet. You could argue that Bitcoin is a more perfect sort of system, but it's not without downsides.
Maybe another crypto-currency will come along and solve these problems. I think I hope it does. But I don't see Bitcoin supplanting modern state-backed currencies. I find it hard to see Bitcoin being used more widely than by the idealogues, the speculators, and those who find utility in it (like Silk Road, but not just that).
1. http://arxiv.org/pdf/1107.4524.pdf
2. http://eprint.iacr.org/2012/584.pdf