Overall, a negative review. I haven't read the book, so I can't argue one way or the other.
Two excerpts -- one is on a specific case, and the other is a general point about the organizational structure of science:
... Goodstein revisits the history of Millikan's oil drop experiment, which provided the first accurate measurement of the electron's charge. A subsequent review of Millikan's notebook suggested that the work might have involved some cherry picking, with only a subset of the complete experimental record ending up published.
Goodstein makes a fairly convincing case that the reanalysis was itself a bit selective. The original work involved using a complex experimental device, and some of the discarded data appears to have simply involved the period in which Millikan was figuring out how to get the machinery to work. It also seems to have been sensitive to atmospheric conditions, and some of the other discarded data involved days where the air quality caused the results to suffer.
These are the sorts of informed judgements that go on in research all the time, but to an outsider they can seem baffling and arbitrary.
... and ...
He also praises the reward and authority systems that help keep the scientific community on the straight and narrow. But it's not hard to imagine that these systems might break down when presented with more challenging cases than the ones presented here. It's also hard to forget that this is a system that has treated Goodstein pretty well over the years; you'd expect him to like it. In less well-documented cases of scientific fraud, the fraudster's position of authority kept people from questioning suspicious results.
In case you are interested