Solubility of oxygen in water with temperature, why does the change in solubility decrease around 40 °C?
The relatively abrupt changes in slope (do a derivative plot to get an even more distinct picture of what is happening here) are due to changes in the solubility function dominating the solubility behavior at a given temperature and $\ce{O2}$ concentration.  For example, Henry's Law will describe the behavior at low $\ce{O2}$ concentrations.  As Henry's Law applies to the theoretical "infinite dilution" condition, this assumption falls apart at higher concentrations.

The greater the concentration of $\ce{O2}$ the more it departs from the ideal infinite solution assumed for Henry's Law behavior.  At higher concentrations, one or more of the different gas laws then controls the solubility.  Based on your graph, it seems that there are three distinct regions, and thus three different gas laws defining the solubility of $\ce{O2}$ as a function of temperature.

One can also take an empirical approach to predicting the solubility based on experimental measurements.  This website has a live "$\ce{O2}$ solubility in water" calculator based on empirical data.  The authors use two different equations for two different temperature regimes: $\ce{0 ^oC - 30 ^oC and 30 ^oC to 50 ^oC}$.  So their $\ce{30 ^oC}$ cutoff seems to agree with the feature at that temperature in your plot.  I don't know the maximum temperatures / concentrations they used for their second equation.