In energy recovery systems, particularly during the incineration process, monitoring of pollutants is crucial due to the potential health hazards they pose to human health and the environment. Let's examine the options provided:

1. Methane: While methane is a potent greenhouse gas, it is not a primary concern during the incineration process itself. It is more associated with landfill sites and anaerobic decomposition.
2. Oxygen: Oxygen itself is not a pollutant; rather, it is necessary for combustion processes. Monitoring oxygen levels is important for combustion efficiency rather than for pollution control.
3. Dioxins: Dioxins are highly toxic compounds that can be released during the incineration of materials containing chlorine. They are of significant concern due to their potential to cause severe health effects, including cancer and endocrine disruption, making it essential to monitor and control their emissions.
4. Nitrogen: Nitrogen, in the form of nitrogen oxides (NOx), can be a pollutant from combustion processes, contributing to smog and acid rain. However, it is not as potent or hazardous as dioxins in terms of individual health risks during incineration.

Based on the examination above, the pollutants that need careful monitoring due to health hazards in energy recovery systems during incineration are dioxins.

Conclusion: The correct answer is Dioxins. They are carefully monitored during incineration in energy recovery systems due to their high toxicity and health impact, which is why they are considered a critical pollutant to manage.