If you mean things like the base rate fallacy, then yes it does.
In the paragraph after the one you quoted, I gave an example of what I was discussing.
If you mean that putting in random numbers for your priors doesn’t solve your problems, then there isn’t any method of considering evidence that fixes that in principle.
You can check the source of the evidence and try to make sure that you’re not putting in random numbers but reliable data.
When considering hypotheses in the real world—like “Does God exist?” or “Is my wife cheating on me?”—Bayes’ theorem doesn’t encapsulate all the skills you need to arrive at a trustworthy answer. You must clearly understand what it is you’re trying to establish—Aquinas’s conception of God is very different from your average Christian’s. You must be willing to question beliefs that you are attached to or identify with—maybe your wife is sleeping with anything that moves, or maybe you’re a needlessly jealous, insecure husband. You must gather as much evidence as possible, including the evidence that you might initially deem to be irrelevant. You must be diligent, fastidious, and detached when performing the investigation—not hiding behind “Oh, my wife would never do that” or allowing your emotions to effect your judgment.
People will have done all the above and still arrived at erroneous conclusions. Such is the difficulty of testing a hypothesis.
If someone believes the Bible is central to question of whether God exists, you can challenge that without having a definition of “evidence” that is informed by Bayes’ theorem.
It could be flawed if there are things that effect the number of phone calls other than Geller’s proposed psychic powers. One show might get more calls but also have more viewers, and that obviously doesn’t make Geller more likely to be psychic during that particular show.
But I am in agreement with you generally with the Uri Geller example. I don’t think phone calls to a television show would alone change my mind, but if we did live in a world where he truly did have psychic powers, I would hope that such evidence would lead me to investigate the matter further.