Measurement error in dependent variable (type I or II error) This source claims that measurement error in the dependent variable leads to more type I errors (page 2, 4th line of text).
However I thought that higher variance of residuals --> larger elements of diagonal of regressor variance covariance matrix --> lower t-statistics / type II errors (failing to reject incorrect nulls). 
 A: I read portions of the excerpt provided. There is a lot there that is very odd. The overall context of the chapter seems strange, touching on several very different topics in short order: ordinary least squares, latent variable models and treatment of outliers.
And what he says about outliers is wrong. In 2.3, the author confuses an outlier (an observation from a "rogue" distribution) with an influential observation - an observation that comes from the distribution of interest, but which strongly influences the estimates. And that concept is further confused with the sobering reality that a genuinely random sample from the population of interest could contain non-representative members, yielding false inferences. Hello type 1 error or type 2 error. So I am not disposed to believe anything this author says about estimation.
But to return to your actual question: I don't know where the double epsilon comes from in section 1.1. If there are 2 sources of error, we should have 2 variables. And the text only mentions one source. In general, you are right. Bloating the error estimate in OLS would shrink estimates of the coefficients and increase type II error. It's just not clear to me why, in this case, the error estimate is enlarged beyond what standard OLS theory allows. Perhaps that is explained somewhere else in the notes.
