I love stef, but he punted on the bitcoin wealth disparity problem when pressed on it.
The wealth disparity problem can not be completely solved by Bitcoin. Right now Bitcoins wealth disparity more or less matches the wealth disparity difference found with fiat because of early adopters accruing more earlier on. There will always be an earning and wealth savings gap in a free marketplace as some people choose to save or work hard and others don't. Sociopaths and con artists may tend to accrue more wealth by preying on the weak and credulous as well, just like with fiat.
Where bitcoin changes things is that is allows for the marketplace to determine winners and losers based upon their efforts, their early adoption, or their ability to convince others (ethically and unethically) to send them bitcoins and removes one tool that the wealthy and/or corrupt use to maintain their wealth: Using the state to manipulate the monetary supply to bail them out, or take corporate welfare, or print more to hand out to their friends, ect...
Without this option the wealth distribution over time should become more fair than currently but will always have differences(as there should be).