* The idea of exponential growth, which seems like an important underpinning of the singularity theory. Nothing in nature as far as I am aware, grows exponentially. Some growth trajectories may for a time look exponential, but they always turn out to be the bottom of an s-curve. The idea that once we develop the first AI with superhuman intelligence, that it will necessarily beget one of even greater intelligence, is deeply flawed for this reason. It is analogous to predicting that Moore's law will continue forever, because ever faster and more capable computers will assist in the design the next generation of chips. At some point the laws of physics will contrain further advances, and we will encounter the upper half of the s-curve.
* The idea of AI in a box. It's the idea that anything we would call intelligence can evolve divorced from a high-bandwidth, real-time sensory apparatus, and divorced from a way to directly manipulate its environment.
* The idea that more intelligence always makes a significant difference. If we look at thinking disciplines where computers are already better than the best humans (chess, heads-up poker, recognizing certain kinds of objects etc.), the differences are small. If the best human's decisions are 99% optimal, say, a computer's may be 99.9% or 99.999% optimal. The point being that a computer can never makes decisions that are better than 100% optimal.