The modeling error in question was independence; that is, if you have five mortgages, each with a 5% change of default, then these can be packaged up as an AAA security as follows: you only lose your money if all five default. A bit riskier package is that you lose if 4/5 default. And so on, each with different returns.
If they are independent, the p(default) = 1/20^5. If they are dependent, it is 1/20. Now multiple mortgage pool size by a 100 or 1,000 or 10,000 (?) and see how far off the estimated risk is. :)
Now combine this with a 30-to-1 leverage when buying these "AAA" securities.
(This was quite a good problem to work through with my daughter to see what that little "independence" assumption means. :)
His main point here was that modeling failures are typically due to out-of-sample conditions; when the housing bubble broke, the markets were might more tightly coupled across the country than the modelers assumed. While they could have seen this kind of dependence if they looked to Japan, there was no such precedence in the US in recent history.