First, he points out that Kurzweil is extrapolating, and extrapolations can be wrong. This seems obvious. And it doesn't do much towards Paul's "isn't".
Second, he says that software and hardware will have to keep improving, and that might not happen. Again, this seems intellectually equivalent to saying "you might be wrong". No evidence is provided that progress will slow.
Third, he says that the singularity will require either a bottom-up biologically inspired model, or a non-biologically inspired "AI" system.
The complexity of the former will take a long time to overcome. Since Allen concedes that sufficient computational power is already here, he seems to be arguing that it will take over a hundred years for us to have a detailed model of the human brain. Looking at the progress of science, this seems terribly conservative, yet little justification is offered. Allen's posited "complexity brake" seems positioned tendentiously — why are we going to start hitting it now, instead of fifty years ago?
As for the AI route, he writes: "But when we step back, we can see that overall AI-based capabilities haven’t been exponentially increasing either, at least when measured against the creation of a fully general human intelligence." What does it even mean to be exponential relative to a binary variable? He is right to say that current methods are limited, and don't achieve generalized intelligence, but offers no reason why that won't happen. His argument seems equivalent to simply saying it hasn't happened yet.
This piece offers little intellectual contribution, and the only reason we're reading it piece is because of the author. It reads like he started from the conclusion he wanted, and threw some paragraphs in that direction. His argument, essentially, is that he's betting against continued progress in science, software, and hardware. That just seems crazy.