I think the problems you described are in two different groups though. The first group, is where we understand everything well, but we don't have the ability to

I think the problems you described are in two different groups though. The first group, is where we understand everything well, but we don't have the ability to track every variable accurately and record the amount of data required, in order to make good predictions. Weather falls into this category. Then there are those like protein folding and animal behaviour where we understand the building blocks, but even of we could track every single building block there would be something missing for us to make predictions.