I was interested to see the comment by Jon Brock because I was one of the initial reviewers of this paper and I identified many of the same methodological problems, plus some other issues with data analysis. I am aware that a third reviewer also raised some of the same points. It is therefore surprising to see the paper published in PLOS One, given the journal's emphasis on methodological rigour.
The field of ERP is blighted by the fact that it yields large multidimensional datasets, giving ample opportunity for post hoc selection of measures. This has been accepted practice in the field, and I put my hand up as someone who has in the past adopted this approach. However, there is growing awareness of the problems this creates in terms of creating a literature full of non-replicable findings. Kilner (2013) has reported simulations that demonstrate how this approach readily yields false positives. This difficulty is compounded if the goal of the research is to relate the ERP to behavioural measures, and a large battery of tests is administered from which a subset is selected on the basis that they give significant results. I agree with Jon Brock that the ERP measure used by the authors in Figure 2 is not the obvious choice for a predictor, either on a priori grounds, or on the basis of results from Phase 1. The subdivision of the autism group using a median split on one of the many available measures in Phase 1 is also questionable.
The words 'reliable' and 'robust' are used by the authors to describe the associations that they report, but this does not seem justified. ERP indices are usually unreliable in individuals, particularly in young children where signal to noise ratio is often low and only a small number of trials can be averaged. If they could show that their ERP measure gives consistent results on repeated testing this would greatly increase confidence in the findings, though we would still need to see p-values of correlations adjusted for the number of statistics computed.
I appreciate that studies like this are extremely hard to do: it can take many years to recruit even a small sample of children, and to persuade families to stay with the study through to follow-up. The goal of identifying early predictors of outcome is important both theoretically and clinically. However, anyone who has worked in this area knows that data from ERP paradigms are usually messy and clearcut associations between an ERP index and behaviour are the exception rather than the rule, particularly when, as in this case, statistical power is very low.

Kilner, J. M. (2013). Bias in a common EEG and MEG statistical analysis and how to avoid it. Clinical Neurophysiology(0). doi: http://dx.doi.org/10.1016...