Ski is correct, the claim that the position of Neptune was predicted through RET is a complete farce. Please read the section in Earth Not a Globe on the subject. It is required reading.
http://www.sacred-texts.com/earth/za/za60.htm
This whole "Neptune is bogus" story is so dumb it had to come from ENaG. Of course.
Ignorant people from the mid 19th century could well believe that Neptune does not exist
because of the doubts about the methods used to discover it. Now it has been seen so many times that the details of its discovery are quite irrelevant. It has been seen by thousands of amateur and professional astronomers, its orbit (and Uranus') have been checked against computer simulations that easily solve the complexity of the non-analytical functions describing the orbits of 8 or 9 large orbiting planets plus the Sun.
Now that I know the source of the doubts about the discovery of Neptune I am most certain that the supposed errors in calculating the orbit of the then-undiscovered Neptune were just understandable imprecision in calculations that had to include some guesswork, and that they at least gave a general area to start looking.
And now that Tom Bishop has given us a reason to compare directly both models, lets look at the relative success of each: real science's model predicts the movement of the planets to within arc-seconds of a degree, for every planet, at any time in the near future. ENaG's "model" predicts the wrong place where the Sun will be at dusk tomorrow, for any place on Earth. And not by a few arc-seconds, but by tens of degrees. That is a difference of about 4 orders of magnitude.
And even if Le Verrier and Adams were totally wrong (which I now don't believe) the perturbations in the orbit of Uranus are real, well measured and well documented. They do predict the existence of at least one planet, which we now call Neptune, and that conclusion was reached by Le Verrier and Adams, and verified by peers.
But Tom Bishop should get his two state of the art, computer controlled telescopes out and punch "Neptune". He does not have to believe Le Verrier, he just has to read the manual in the page where they tell him how to set up the telescope, and then he can see that there is, in fact a celestial object where Neptune should be, and then he can check for himself that it moves with respect to the stars. Or maybe he does not have the telescopes he says he has?