From what I've gathered about the math behind these curves, I don't think there are good answers to the concerns you are raising vis error analysis.

Hubbert was not a mathematician or an econmist.  He drew his curves by hand, and calculated the areas underneath them by counting the squares on his graph paper and guessing.  He assumes logistic growth and decline, and some of the field curves look like logistic curves.

But I'm not seeing a lot of advanced statistical (or econometric) methods or models yet from the peakers.  Drawing and fitting curves is meaningless - its the equations the curves reflect and the relation of the variables in the equations to the facts in the ground that provide meaning.

Got it - it is certainly true that because of the Q term, the fluctuations are much smaller to the left than the right. However, that doesn't prevent the curve from diverging from the model if indeed the model is wrong. More tomorrow - I now have a couple of countries where it doesn't work that we can chew on.