I have my concerns about the whole premise but essentially Paul Romer is advocating we try what the Dutch East and West India Company in the 16th century all over again (of course, without the slaves, indentured servants and coercion) 

It's not that bad of an idea and one that forces us to think what is possible and how can we make the world better.  That's what the TED talks are about anyway, spreading ideas.  

I thought immediately about how else charters could be applied:

– Charter new businesses under rules that they MUST adhere to on environment, profit sharing, executive pay.

I know we do this today somewhat, but they are laws. You have to comply or work around them.  In the charter system, the company opt-in for the funding.

– Allow current successful cities to extend their current city charters to new countries.  i.e. Wouldn't it be cool if there were a New York City in Nigeria, Romania and China that ran under the cities rules with our expertise.  
Yes, it's my fantasy to see New York City rule as a city-state like Athens, Sparta, Rome or Singapore, but so what? It's called civic pride!

– Create bank charters that are contingent on ONLY investing locally.  Say a 5 miles zone around the bank. Communities can be built with ethical banking.

Again,  I keep going back the Bailey Savings and Loan from 'It's a Wonderful Life'.  If there were a bank like that where you live, wouldn't you use it?

Those are just the three off the top of my head,  what can you think of?  (Regardless of what you think of, you should watch the video.  It's fantastic.) 

One more time with the link:

Paul Romer's radical idea: Charter cities