None of this changes the fact that there has been found a lineage of transitional fossils demonstrating the evolution of whales from land mammals, or the fact that the inactive vestiges of the genes that control the development of limbs have been clearly identified in cetaceans (as explained in this article).
Of course there are many details that evolution has not yet explained. Curious, though, that no matter how important a discovery is made about the evolution of life on earth, that creationists always try to distract attention to points that remain unknown; that's because the information that is known doesn't bode too well for creationism. </understatement>
(Ignore that man behind the curtain!)
From what I can tell (admittedly only from quick googling) it is NOT apparent at this time what, if any, neural structures may be present in cetaceans that allow this. This is a hot topic, but the research still seems to be in an early stage.
It also seems far from clear that cetaceans have "full function" during these periods of "drowsing," when they close one eye and the opposite side of the brain reduces its activity levels. In fact they often sink a bit in the water and seem to loose some function. It may provide just enough wakefulness to alert them to predators and remind them to breath. (NOTE: Breathing is a conscious activity for cetaceans. In humans, and other land animals, it is an automatic function that does not require consciousness.)
In any case it's not yet clear that there are any drastic physiological/neural differences behind this capability. It may just be (in the typical fashion of evolutionary tinkering) a slight modification, or modified usage, of structures already present.
And that seems to give you satisfaction. Yes, there is much about biology we don't understand, but we're understanding more every day. Whereas that ol' book is just the same as it was 1700 years ago.