Some of those atmospheres and the changes described seem a bit odd to me. I think a bit more of Jim Lovelock's thinking needs to be injected here, or at least the explanations made a little less facile.

The early "Epoch Zero" atmosphere of Nitrogen (neutral), CO2 (weakly oxidising) and H2S (strongly reducing) is clearly out of balance and there is no mechanism presented for maintaining that imbalance. Lovelock argued strongly and successfully that atmospheric imbalance is almost inevitably the consequence of life. Mere inorganic processes don't have the rate constants to generate large enough volumes of dissimilar gasses simultaneously. I can't see any easy way out of this problem and suspect that either the science is "wrong" or it is so briefly quoted that some subtle and complex mechanisms have been entirely glossed over.

In the transition between Epoch Two and Epoch Three, photosynthetic Oxygen is claimed to be responsible for clearing out the Methane (yes) and CO2 (no!) from the atmosphere. Whilst free Oxygen makes a great scavenger for Methane (a simple redox reaction), CO2 is already fully oxidised and the presence of extra Oxygen is simply irrelevant. (were this not the case, global warming opponents would be able to argue that CO2 added to the atmosphere would be removed by virtue of the oxygen already there - though the rates might not be adequate, but that's never stopped pseudo scientists arguing one way or another) The error has been made of ascribing one change as a cause of another when in fact both are caused by some other factor:-

Instead, it is the geological process of burial of dead organic material with its reduced carbon content that simultaneously consumes the CO2 from the atmosphere and releases free Oxygen. Here, I think the error lies in the brevity of the report, but it's a crucial mis-statement of the science.