What effect does the mno2 catalyst have on the rate of evolution of o2 gas?

You did not specific if the evolution of O2 gas comes from the decomposition of hydrogen peroxide. But I assume it is, since MnO2 is commonly used to increase the rate of hydrogen peroxide decomposition to water and oxygen.

Thus MnO2 increases the rate of O2 gas evolution, but the amount of O2 gas evoluted is the same. It does so by providing an alternative reaction pathway via a transition state with lower activiation energy.