I was looking at the Draper & Smith's 'Applied Regression Analysis', as did the person who asked:this other question on CrossValidated
In short - the variance-covariance matrix of the residuals in regression is given by $(I - H)\sigma^2$, where $H$ is the 'Hat Matrix'. So in general we must assume the residuals are not independent.
Yet whenever I read about the assumptions of regression it says the error terms should be independent (as well as having zero expectation $E[\epsilon_i] = 0$ and equal variance $Var(\epsilon_i) = \sigma^2 \forall i$.
I am missing something, or using a loose definition - my naive, inexperienced reading of this looks contradictory. Thank you, Chris