Basically all Sornette has done is an exercise in pattern recognition. It's almost not really forecasting at all, since he doesn't predict when a pattern will emerge.
"The problem is with the idea that you can forecast economic results."
What is the problem? I'm willing to go out on a limb and say with confidence that manufacturing activity in this country will not grind to a complete halt tomorrow. I could be wrong though. We could be hit by an asteroid or something arriving from sunward.
It's not at all a question of whether you can forecast economic results, but rather how far into the future and with what confidence interval.