Mercury (Hg) is globally recognized as a persistent chemical contaminant that accumulates in marine biota, thus constituting an ecological hazard, as well as a health risk to seafood consumers. Climate change-related stressors may influence the bioaccumulation, detoxification, and toxicity of chemical contaminants, such as Hg. Yet, the potential interactions between environmental stressors and contaminants, as well as their impacts on marine organisms and seafood safety, are still unclear. Hence, the aim of this work was to assess the bioaccumulation of Hg and neuro-oxidative responses on the commercial flat fish species Solea senegalensis (muscle, liver, and brain) co-exposed to dietary Hg in its most toxic form (i.e., MeHg), seawater warming (ΔT°C = +4 °C), and acidification (pCO2 = +1000 µatm, equivalent to ΔpH = −0.4 units). In general, fish liver exhibited the highest Hg concentration, followed by brain and muscle. Warming enhanced Hg bioaccumulation, whereas acidification decreased this element’s levels. Neuro-oxidative responses to stressors were affected by both climate change-related stressors and Hg dietary exposure. Hazard quotient (HQ) estimations evidenced that human exposure to Hg through the consumption of fish species may be aggravated in tomorrow’s ocean, thus raising concerns from the seafood safety perspective.