I've spent a couple of posts criticising the book mentioned in the title. I think criticising is more important than agreeing. Agreeing just takes an 'Okay', criticising needs more work: you need to explain where the chain of reasoning breaks off. But still, it may be of some use to make explicit the points that Mazzucato makes in her book that I endorse.
Firstly, we have an explanation and rejection of the linear model of innovation. This is the idea that advances in technology and science go from basic science to applied research to development. In reality, as she conveys the consensus view on this, things are not quite like that: reality is messy, and you get feedback loops everywhere. Newer science enables you to build better technology, which in turn help you do more science. Or new technology is invented by tinkering or serendipity, and then science has to come and explain what just happened.
Secondly, we have her discussion of vision and the role of ideas. She emphasises the importance of what people think of different things. She argues, for example, that if people see the State as a slow bureaucratic elephant, smart people won't get drawn to it, setting off a self-fulfilling prophecy. And vice versa: if people think the State is cool, people will be eager to work with and within it. She wants people to have a positive image of the State to make its entrepreneurial job easier. I'd just want to note that many top public institutions and research agencies are well regarded (Think NASA, DARPA, the US National Labs, or top public universities), so one reason why you have that much talent there is halo effect, possibily seeded initially by large funding availability. The same probably happens with Defence contractors (weaponry is cool). So the State may be seen as a slow elephant by some, but certainly not the public research institutions are seen like that.
Thirdly, we have her lenghty list of examples of what the State has done. We should rather be precise and talk about each individual event in a case by case basis (talk about funding, researchers, institutions, knowledge transfer, etc) rather than just say 'the State did this', but the fact remains that you can't understand the state of modern Science and technology without taking into account that. I already knew most of what she is telling, but others may not. Some may have thought that, say, the computer industry all happened in garages, and that's plainly wrong.
We then have her pointing out that systems of innovation are important, that it is not just about the individual pieces working nicely, but them working nicely together. Think a football team made of brilliant but uncooperative players. You have a poor system made of nice individual parts. Of course you can dispute attributing niceness to a part of a system that doesn't work well in the specified system. In practise, the focus on systems means to pay attention to the interrelations of the different parts: what happens at the contact points between Academia, industry, the government, financial markets, and so on. The Systems of Innovation perspective has its critics, but it is well regarded in the mainstream of the economics of innovation profession. Mazzucato does not exactly endorse the theory, as she says that it gives the State a mere passive role, but this is the mainstream theory she would be closer to. The critique here would be that Mazzucato focuses too much in one agent in detriment of others, but this is sort of justified on her view, given that she sees that the State is an underfocused agent.
Finally there are some policy recommendations that seemed reasonable, but I'll leave this for a future post discussing her policies.