Summary of problems:
Scientific explanations are judged by their ability to make accurate predictions of new data. Explore Evolution obscures this point by stating that "The best explanation will be the one that explains more of the evidence than any other" (p. 5). This claim sneakily twists the student's understanding of how we evaluate scientific explanations. Doing that is necessary to get the subsequent erroneous claims through the door. It also cracks the door for a discussion of the supernatural in science classes, since the suspension of natural law can explain absolutely anything (making it useless as a scientific prediction).
To be scientifically useful, an explanation ought to do more than merely explain existing observations. A good hypothesis may begin as an inference drawn from known facts, but it also must make some predictions which lead us to new observations. If the observations are not what we predicted, we can reject that hypothesis, but we do not regard it as proven if the observation is as predicted. That predictive power is part of what allows us to evaluate the quality of a scientific explanation.
The evidence in Explore Evolution would not allow us to distinguish between multiple hypotheses about who washed the car in their chosen example, nor is it impossible that some mischievous gremlin planted all of that evidence merely to make it seem as if someone washed the car.
Indeed, that latter hypothesis could explain any set of evidence we might possibly gather. It does not, however, predict the details of any new observation at all. That doesn't mean it's wrong, but it does make it a worse explanation than a hypothesis which makes testable predictions. This would be true even if it explained existing observations which existing theories did not explain, of the existing theories had a track record of producing correct predictions.
Philosopher Elliott Sober uses gremlins to make a related point:
You and I are sitting in a cabin one night, and we hear rumbling in the attic. We consider what could have produced the noise. I suggest that the explanation is that there are gremlins in the attic and that they are bowling. You dismiss this explanation as implausible. I hope you see that, If there actually were gremlins bowling up there, we would expect to hear noise. But the mere fact that we hear the noise does not make it very probably that there are gremlins bowling.Elliott Sober (2000) Philosophy of Biology, 2nd ed., Westview Press:Boulder, CO. p. 32
Sober's point is that the gremlin hypothesis may be likely, but it is not plausible in part because it is not likely that there are gremlins in the attic to begin with. Thus, an explanation which seems to explain more evidence can be a worse hypothesis if it fails to make novel predictions, or if it requires us to invoke unlikely phenomena, such as the existence of gremlins.
Explore Evolution offers few hypothesis about biology, preferring to attack existing explanations. But where it does offer alternatives, they tend to exhibit the same flaws as the two "gremlin" hypotheses offered above. For instance, EE suggests that there may be multiple trees of life arranged in an "orchard". The gremlin(s) which tend that orchard could undoubtedly have planted it in any way, and they could have been planted in a manner which produces a pattern of modern diversity indistinguishable from what we would find if there were a single tree of life (which is to say, indistinguishable from what we actually find). A hypothesis involving multiple trees of life requires us to understand multiple origins of life, and a hypothesis involving an orchard of trees (rather than a forest) requires that we hypothesize something capable of planting and tending all of those trees. The orchard hypothesis and the single tree hypothesis might both explain all the extant data, but to hypothesize an orchard raises more questions than it resolves, while making no novel, testable predictions in its own right. This makes it a worse explanation, and these flaws would persist even if it could account for observations that existing hypotheses cannot explain.
Again, the misrepresentation of basic issues in the nature of science invalidate the book, even if the misrepresentations were not clearly intended to open the door to nonscientific ideas in the science class.