I think look at people's experience with the oxydator, as multiple people have shown it releases small amounts of H2O2 continuously.
I think my specific concerns would be (ranked from most to least significant)
1. that some crucial Trace elements that are needed by everything are reactive with H2O2, and so could have their oxidation state and thus their solubility and bioavailability changed, often made lower. This, as much as direct cell killing might be a reason that H2O2 can reduce the amount of algae growth in a system.
2. Not all algae species are equally susceptible to chemical oxidation, some like cyanobacteria are more sensitive. So I would expect the community of what photosynthetic organisms grows to change when dosing peroxide. This might not be bad. It might be exactly what is desired, but it might be difficult to predict all the ramifications, such as decimating copepod population.
3. As far as direct cell killing, I would certainly expect the population of bacteria in the water to change, some would be very susceptible to peroxide, and others less so. This, again might not be a concern. But it is a change that is hard to predict, and hard to know if it is happening, and might have some unexpected consequences for things like how nutrients are processed in the system.
