Lets begin with the state of the art. The voice and face recognition technology is the same as what defeated human players in Go. While it is not yet the same kind of general intelligence as humans it proves that you don't need the same number of neurons and connections as a human to be very very intelligent in at least a narrow domain. They are true intelligence by any measure, just not as general as human intelligence. Furthermore human level intelligence is not required for machine intelligence to be a problem. The level of AI we have now will already replace millions.
"Nothing in the state of the art of AI today is going to wake up and decide to kill the human masters." - and nobody is suggesting it will. It is almost like you have listened to nothing that has been said. Virtually every presentation by the likes of Gates, Musk, Harris and Hawking is prefaced by a statement to the effect that the Terminator view of AI isn't credible. This is a classic straw man argument, a misrepresentation of your opponents position. AI is a threat, but not because they will raise armies of mechanized soldiers to exterminate us.
"Despite appearances, the computers are not thinking. You might argue that neural networks could become big enough to emulate a brain." - Machines will 'emulate' a brain in the same sense that a F16 emulates a seagull. Nobody will argue that a F16 replicates the delicate structure of the feathers of a seagull, but if I had a choice between a seagull and and F16 in a fight.... machines already outperform us in many narrow domains. I think my dog is conscious and 'intelligent', but it can't walk the right side of a pole when on a leash.
"Maybe, but keep in mind that the brain has about 100 billion neurons and almost 10 to the 15th power interconnections." - Current neural networks were inspired by, but not attempting to simulate human neural activity. Just as human flight is a combination of principles inspired by nature and our mechanical expertise, aka the internal combustion engine, artificial intelligence is not a simple minded replication of the human brain neuron for neuron. It might be that the human brain is grossly inefficient, with many neurons and connections being uninvolved. There is no reason to believe that achieving human level intelligence requires a specific number of neurons or connections.
"Worse still, there isn't a clear consensus that the neural net made up of the cells in your brain is actually what is responsible for conscious thought." - unless you are referring to clergy I'm afraid I have to call this utter bullshit. There is no magical 'soul' separate from the brain. The neurons in our brain and the configuration of their connections make up who we are. We may not really understand consciousness all the way down yet, but there is no doubt that it is an emergent property of the configuration and activity of neurons.
"There's some thought that the neurons are just control systems and the real thinking happens in a biological quantum computer..." - The 'real thinking'? I'm sorry, but this is just outright magical thinking. Replacing the theist 'soul' with 'quantum computer' does not help. Even if there were a quantum mechanical aspect it is neural networks which enable brains to do what they do, not QM.
"Besides, it seems to me if you build an electronic brain that works like a human brain, it is going to have all the problems a human brain has (years of teaching, distraction, mental illness, and a propensity for error)." - finally something we can agree on. Yes, a machine that learns will have the same weaknesses we do potentially. They will just be more intelligent. They will not have the same limitations.