I could imagine that a very thin piece of paper could find its way between the cracks. It causing damage by resting on something I imagine is slim. The paper wont catch fire (having an autoignition temperature well in excess of a computers operational limits). Arcing to the paper I think is unlikely if not impossible given that it will always be in contact with some part of the computer to maintain charge balance. In addition paper is non-conductive so it will not cause a short anywhere.
The only thing I can personally think of is that the paper may migrate it's way to your fan and jam the fan which could easily cause a chain reaction of what I would call bad things.