Perhaps one of the flaws is less with the structure of the models and more with the stochastic specifications used to give the models empirical content. Most of the models I have seen are fed shocks that follow a gaussian distribution. But we have known for half a century now (John Tukey, Benoit Mandelbrot) that real-life economic and financial shocks are fat-tailed. Extreme events will occur far more frequemtly than a gaussian distribution will predict.
The primary problem in my view is not that economic models are flawed (although that too) but rather that the average economist has a rather poor mastery of statistics. That leads to serious underestimation of volatility and to parameter estimates that are very unstable.