We present a joint theoretical and experimental investigation of charge doping and electronic potential landscapes in hybrid structures composed of graphene and semiconducting single layer molybdenum disulfide (MoS2). From first-principles simulations, we find electron doping of graphene due to the presence of rhenium impurities in MoS2. Furthermore, we show that MoS2 edges give rise to charge reordering and a potential shift in graphene, which can be controlled through external gate voltages. The interplay of edge and impurity effects allows the use of the graphene-MoS2 hybrid as a photodetector. Spatially resolved photocurrent signals can be used to resolve potential gradients and local doping levels in the sample.