There are fundamental structural issues in the car business. Although many of these are mirrored in other industries such as supply chain narrowing (like how a fire in an obscure factory can bring down a silcon foundary business or a flood in thailand can make disc drives scarce), there are a few that are specific to the car biz.
One issue with the car industry is that because of certain union contracts, GM often was unable to easily modify production to meet demand (resulting in non-optimal inventory for demain and creating pricing problems that affected profitablity). Another issue was the maze of dealer protection laws (some of which tesla is experiencing) that created issues with providing steady sales volume of popular cars.
The biggest structural problem in the demand for cars is that financing (the grease that makes the car transactions work) dried up. A healthy company could have perhaps mitigated this by temporarily providing dealer or factory financing options, but GM (and ALLY aka GMAC) wasn't able to scare up enough liquidity to make that work. This is probably the most similar to the 1930's situation in which the governments probably actually exasparated the credit crunch. People familiar with this wanted the government to avoid that mistake. It's perhaps not a comparison, more than a lesson learned from the 1930's.
There are some other things that are mostly just mismanagement (e.g., aggreeing to unsustainable employee benefits when profits were high and not investing enough in forward looking technologies), but these probably aren't enough to bring the house down in a slow-down, but provided enough of a boat-anchor in combination with the structural problems that tipped over the boat.
Some say the car problem (the fact that cars are often financed at mostly vertical market rates rather than broad-based rates) is a lesson for the housing problem (which is financed mostly at government intervention interest rates because of tax-incentives). As long as financing is not market rate, it is easy to get quickly out of equilibrium both ways because financing is highly leveraged. People talk about limiting the ability of banks to speculate with deposits backed with estimates of future income, but ignore that is exactly what most of the population is doing with thier savings when they buy a car, house or expensive vacation. Nobody however, seems to be talking about legislative limits on how the population can destablize the economy with thier borrowing habits and forcing people to have some minimum liquidity ratio.