One of the major mistakes is that technology is not universally disruptive. It's main disruption arises from unexpected forms of technology, not the ones we pay attention to. I.E. we get cellphones, not flying cars/jetpacks.
The progress tends to be in areas that were not gaining progress before,
In general the Singularity people believe the progress will entirely be in AI. Specifically, they think that our advancements in computer technology will continue to be in complexity etc. along the SAME lines it has already done. I hereby propose that AI will NOT have any major disruptive changes in the future. Instead it might be in something dramatically different. Maybe shoes, soap, or some other commonplace item - kind of like the phone underwent a dramatic and unpredicted change.
The major issues with the AI people is that they think all the progress in making computers have faster processing of mathematical equations will somehow create a thinking computer. We see it all the time in all the fiction. They confuse good at math for "have a soul".
Most importantly, while the Singularity people talk about unable to predict, they then go ahead and make a bunch of crappy predictions - mainly based on junk science that we know is wrong.
You want a realistic story of the creation of the first AI. AI gets created, learns to talk, explores the internet then writes a horrible, "emo" suicide note before it kills itself.
THAT would be far more likely than the crappy "humans uploads the entire race and stops having kids" junk that Singularity people like to fantasize about.