1. I think the author is probably talking about the **residuals** of the model. I argue this because of his statement about adding more fourier coefficients; if, as I believe, he is fitting a fourier model, then obviously adding more coefficients will reduce the autocorrelation of the residuals at the expense of a higher CV (because of overfitting). In this context, autocorrelation on the residuals is bad, because it means you are not modeling the correlation between datapoints well enough.
 2. The main reason why people don't difference the series is because they actually want to **model** the underlying process as it is. One differences the time series usually to get rid of periodicities or trends, but if that periodicity or trend is actually what you are trying to model, then differencing them might seem like a last resort option. 
 3. This really depends on the area you are working on. It could be a problem with the deterministic model also. However, depending on the form of the autocorrelation, it can be easily seen when the autocorrelation arises due to, e.g., flicker noise, ARMA-like or if it is a residual underlying periodic source.