> 1. Using the unadjusted figures...
The adjustment is to correct for sex. This is explained in the original paper and supported by their data: The males in the study had higher lead levels as children and males in general are more likely to commit crime, this alone causes a correlation between lead and crime.
Correcting for sex is not "unusual": it's done in 99% of research on human subjects.
> 2. Using the adjusted figures, there’s a clear association of lead levels with later criminal convictions, and the association is effectively statistically significant
The authors perform comparisons of blood level with 5 different crime statistics and only 1 is statistically significant. These comparisons must be considered together: What causal effect between lead and non-violent crime would not also apply to violent crime, crime as a whole, first-time offences, or repeat offences?
Relevant xkcd: https://xkcd.com/882/
> 3. Using the adjusted figures, there’s a clear association of lead levels with self-reported offenses, but the statistical significance is poor.
The author bases this conclusion from their chart of self-reports vs lead at different ages, which does not (as they claim) use the sex-adjusted figures. The statistical significance is indeed poor for the adjusted values, they got that right.