In my experience, one problem that seems to be pervasive is polarization. There seems to be a lot of, "Well, if one psychic is BS, then all psychics are BS." There's also the even more subtle, "Well, this psychic got this one detail wrong, so the rest has to be wrong, too."
The first logical fallacy is pretty self-evident, but the second one is far more insidious, and easy to fall prey to.
Even when I talk to my own guides about me, I'll mess up the channel and insert or change words in ways that they didn't mean. Sometimes it will just be one word or so, and they'll just pick up where I interrupted and patch over it to make sense. Other times, they'll correct me if what I ended up getting changes the message too much. Still, they don't always correct me. Sometimes I end up a sentence or few that make no sense at all, or that contradicts something that was just said. Sometimes at this point they'll throw up their arms and say something like, "look man, that was all you. Start over from here ->.", but occasionally they'll let it go, leaving it as an exercise to the reader.
That would be some serious fodder in a reading with a skeptic. I'm pretty sure that practiced, professional, legit psychics have this problem far less frequently, but I also doubt that it goes away completely.
If people didn't polarize so much, and kept what was useful as being useful, and discarded what wasn't, things would be easier. I'm biased, however. My days of being a completely dismissive skeptic are quite over.