The major grudge against Bitcoin seems not so much to be that it isn’t backed by anything – remember, we’ve already established that most currencies, and therefore economies, aren’t backed by anything – but that it isn’t regulated by any established (read: government) body.
Yes, cryptocoin at this stage is going to be used for illicit purposes. But as its use becomes more established and more widespread it will have the capability to police itself. Illegal use of the currency will continue, as it does with any currency, but will diminish in proportion to its uses in legal commerce.
There certainly are things to fix, be it in Bitcoin 2.0 or some other cryptocurrency. Anonymity must continue while verification and accountability must increase. A larger market will probably stabilize volatility, while annoying governments who will not be able to control international or P2P transactions. Ultimately it may prove to be a most stable currency as it will only be affected by market demand and not domestic or political issues.
An international currency not affected by external inflationary conditions or conversion rates and fees might be the next driver of global economic growth as corporations and individuals find it easier to engage in trade. Imagine the stock price of an Apple not needing to offshore its horde if it could move operational funds around much more easily.
Reducing transaction latency is crucial for this to be a real-time currency. Fragmentation of the blockchain with ongoing reconciliation will speed this up, while the system will still be able to detect and reverse fraudulent transactions.
Finally, BTC2.0 miners should be rewarded for real work. All of that computing power can be put to good uses such as advanced simulations of protein folding (cure for cancer, anyone?), verifying blockchain entries, finding the next digit of Pi or the next largest prime number, which certainly has its applications in strong cryptography, helping to complete the Bitcoin circle.