What I really don't get is why anyone would criticise fiction for lack of realism, unless it is try to be as realistic as possible (I'm guessing Believe isn't attempting to be realistic given the extensive telekenesis). A good story, interesting characters, excitement, watchability, interesting relationships... none of these things need an ounce of realism to make them work (some internal consistency within the programme might be needed, but nothing more than that.) Note - I'm not ready to stick my neck out and say that Believe has a good story, interesting characters, excitement or interesting relationships- but it does have a bit of watchability.
http://en.wikipedia.org/wiki/Suspension_of_disbelief