There was nothing wrong with using Black-Scholes to price stock options. The problems started when people started using it to price their own Grandmothers.
Simple models also assume independent variables, because dealing with cross-correlations for thousands of stocks is hard. This is a mathematical statement of the 'common sense' expectation that you loose a little, win a little. However, in reality the market is highly correlated, for example in the last year virtually everything has gone down.
This is pretty common knowledge in the research branch called 'econophysics', google it. It's an interesting field, one of their major 'result' is that classical economic theories are fairly flawed, and only seem to work because they are like self-fulfilling prophecies (traders implement their beliefs, but only up to a point!).
They tried fixed income arbitrage with very high leverage. Black-Scholes ONLY applies to options.
The work that won the Nobel Prize had nothing to do with the downfall of Long Term Capital Management. Get your facts straight.
Variations of Black-Scholes are still used successfully in the trading world. The only difference is that no one thinks that returns follow a normal distribution anymore (but the Black-Scholes formula allows you to choose any probability distribution you want).