There is a vast literature on reasoning and rationality that tries to understand what "good judgment" consists in. It includes Michael Polanyi's work, which is still very much respected among some philosophers, especially those influenced by Ludwig Wittgenstein. But the literature starts (in the Western tradition) with Plato and Aristotle's ideas about knowledge and continues through contemporary work on scientific methodology.
The quick answer to your question is that most people have more self-confidence--even arrogance--than you seem to have about their opinions, especially if they are "experts." So, they might be wrong, but they don't worry about it like you do (as my husband the surgeon says about surgeons "sometimes wrong but never in doubt"). A more thoughtful answer to your question, which draws on epistemological ideas, is that so-called experts--just as non-experts--are susceptible to various kinds of bias, such as confirmation bias (evidence for one's position is weighed more heavily than evidence against) and salience bias (one's personal experiences are weighed more heavily than the experiences one has merely heard about). And so-called non-experts can in fact be more knowledgeable than so-called experts about their own experiences of e.g. what it feels like to be poor. So, you shouldn't defer to the experts, although you can sometimes learn from them.
There is now a philosophical literature on "peer disagreement" which covers the question of what you are supposed to do if your "epistemic peers" (other experts if you are an expert) disagree with you on a topic.
Knowledge may be valuable in itself i.e. for its own sake. When you ask "What is the value of knowledge?" you may be asking what else is it valuable for. There is hardly any human activity that is not aided by relevant knowledge. Medicine and technology are the result of applying scientific knowledge to a vast range of human needs.
Questions should be understood contextually. In your story about John, we are led to assume that John is about to drink the contents of the glass, and not, for example, use it in a chemistry experiment requiring high levels of purity. The suggestion is that it is water and not e.g. orange juice or beer. A small amount of harmless impurities don't make any difference to its drinkability-as-water. A tiny amount of cyanide, however, makes all the difference in the world to its drinkability-as-water. It's not the amount of impurity that matters, its the difference the impurity makes to our intended use of the water. (This is a case that shows the pragmatic functions of language. Sometimes you miss things if you take language "too literally" i.e. devoid of context.)
Some recent papers by the psychologist Daniel Kahneman suggest that we are not very good at predicting what will make us happy. It is a good idea to read these to get a feel for human fallibility.
Philosophers often argue that reflecting rationally on our values and goals can lead us to pursue what we "really" want, and thereby lead to greater satisfaction. You might try this and see whether it helps.
Some Buddhists, and some psychologists, argue that pursuit of a goal is more exciting than achieving it. They suggest focussing on the activity rather than the desired result.
If Mediums did get "results" then it would be rational to go to them for advice i.e. not a waste of time!
So I think the thing to focus on is the results, and ask the question, are the amazing pronouncements just coincidences and/or wise vague sayings? There's no shortcut to answering this--it is an empirical question. Remembering of course, that Mediums, TV and authors don't always report reliably.
It is true that we can only see/interact/cognize as human beings do. But it does not follow that knowledge is generally "biased." Particular biases (that we can discover through cognitive psychology, social analysis etc and check for) may lead to specific faulty knowledge claims. We do our best: we check for the biases that we know humans make. Animals/extra terrestrials might see/interact/cognize differently. We can learn about them, and see how their knowledge might differ from ours. There is no perspectiveless point of view (some philosophers call it a "God's eye" point of view).