Under what circumstances has substantial state intervention into the economy been helpful and in what cases has it had negative effects?
This is an exceedingly difficult question to answer with any certainty. It is not always clear when government intervention is helpful and when it is not. For example, it seemed that government intervention in the Japanese economy was wildly successful in the early 1990s, but the Japanese economy crashed not long afterward and we now think the government was excessively involved. That said, we can at least speculate that government intervention is most helpful when an economy is newly industrializing. After that, it can be less and less useful.
To think of how this is so, let us think of some major success stories that seem to be attributable to government intervention. In the 1860s, the US government massively subsidized the construction of railroads. This was at a time when the US was industrializing. The subsidy helped to cause a widespread network of rails to be built and the American economy boomed. After World War II, the economies of Japan and Singapore similarly boomed. In both cases, the government was closely involved in guiding the economy. In both cases, the growth was driven by industrialization. Later on, we saw similar things happening in South Korea and China.
After a country has industrialized, it seems harder for government to effectively steer the economy. It appears to be harder for the government to pick which industries should be supported than it was when the country was industrializing.