re: Winklevoss Twins Plan First Fund For Bitcoins

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What are these "current bottlenecks"?

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It's difficult to buy and sell bitcoins, just as the article stated. There are exchanges setup all over the world that allow you to do this, but the red tape you have to go through to get legacy money to those exchanges is pretty significant. Once you have bitcoins, however, sending them to individuals or business is extremely easy.

It's also true that there aren't many stores and sites that accept it yet, but that number continues to grow every day.

As for the technology flaws, well, bitcoin is a protocol and it is secure. However, third parties that deal in bitcoin have been hacked and bitcoins have been stolen from them.

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Why is it necessary to solve a complex mathematical problem in order to obtain bitcoins?

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It's a concept called proof of work. It secures the bitcoin network and allows for the processing of transactions. The system rewards people who perform this work with "mined" bitcoins as well as transaction fees for the transactions they process.