I'm not necessarily sure that verifiable proof of the existence of telepathy would turn the laws of physics upside down. Telepathy is the ability to communicate via some means other than by use of the classical five senses. Its impact upon physics would be far less than the implication within neuroscience and biology. Telekinesis on the other hand, which is the ability to act upon a physical system by will alone, would.
If you consider that we've developed means by which to transfer information 'invisibly' using technology, it wouldn't take a great stretch of the imagination to consider how telepathy might be possible. But to the best of my knowledge, there hasn't be any 'verifiable' proof, a necessary condition for telepathy to be considered scientifically. Though I'm not familiar with the aforementioned discussion between Sheldrake and Dawkins, perhaps the reason for Dawkins' perceived closed-mindedness is that the 'evidence' provided wasn't deemed sufficient to draw the conclusion that telepathy exists, and what 'evidence' was provided wasn't verifiable.
This leads me to question, what evidence do you have that telepathy exists? Keep in mind that a belief doesn't necessarily constitute science; the belief must be backed by some empirical evidence that can be repeated by others using the same methodology.
Now I would have to agree that there is a great deal about the reality in which we live that is not yet understood by mankind. It would be enormously arrogant for us to assume that our present understanding of the universe is absolute. We've been wrong before and therefore we must be open to new possibilities. But the scientific method must be observed as well. It is also possible that not all truth can be discovered by means of science. Nonetheless, with regards to telepathy, I've seen no convincing evidence so if you have it, please share.
Edit: As 'Bob' mentioned above, there are scientifically valid theories that could explain telepathy, as well as other phenomenon such as time travel (though not necessarily in the context that sci-fi has familiarized us with), that haven't yet been accepted by the larger scientific community. Furthermore, I'm aware that there has a been a significant amount of research in this field. At the present however its still considered more pseudoscience than real science. From personal experience I know that the technology that we use every day is lagging significantly behind what's being developed at universities, government-funded organizations, and private companies. We must remain open-minded, yet reasonably skeptical, of new possibilities.