Rather than attempt to reply to everyone individually with quotes all over the place I'll try and do this all at once.
The goal for me in this exercise is to find shows, whether recent or past, that adhere to our scientific understanding of the world as we know it today.
Do I allow open the door for the 'possibility' of psychic phenomena... yes. But... science as it stands right now says that that is highly unlikely. There are NO instances of psychic phenomena that has stood up to rigorous skeptical scrutiny. Science demands that an idea has to be testable. At which point it needs to be tested over and over and over (and yes we're talking about double blind experiments). If the hypothesis fails, even once, it is discarded as false and we either refine the hypothesis or toss it away.
I've never heard of a case of reported psychic phenomena standing up to that kind of rigorous testing. How many faith healers, psychics, tarot readers have been shown to be charlatans once put in to a double blind experiment. How many have allowed themselves to be tested in this manner?
Science is about rigorous testing. Science also proves nothing (ever!). All it does is lend support to a hypothesis. Once it's gone through the testing loop enough times it becomes accepted as a theory. Not a proof, a theory.
I don't see any problem with holding this standard up to science fiction.
Someone made a good point about the fact that we haven't discovered life on other planets and hence any show that depicts otherwise is pseudoscientific and/or supernatural. Point well taken. We haven't. We're searching, but we haven't yet. I suppose this is where we have to look at the term "speculative fiction"
Now is it any less speculative to say we may learn that psychic phenomenae may be found to potentially exist as it is to say life on other planets may exist. In some sense no. But, I would personally argue (and this is only my opinion) that at least the notion or possibility of life on other planets at least fits into the realm of possibility from what we know of biology, chemistry, etc... Much more so than the notion of someone levitating a spoon or reading my thoughts by thinking really hard. There's just no support for it in science.
But, you ask, can't the same be said for life on other planets?
Let's look at the case of shrimp living near undersea thermal vents. Until recently it was assumed that no life could exist under such extremes. And yet there it is, right on our own planet. This lends support
to the hypothesis of other planets with similar extremes could potentially be true. I've seen no such supporting evidence in the case of psychic phenomena e.
I hope that helps in understanding where I'm coming from with this. ALL the replies so far have been great!