Van der Waals structures formed by aligning monolayer graphene with insulating layers of hexagonal boron nitride exhibit a moiré superlattice that is expected to break sublattice symmetry. Despite an energy gap of several tens of millielectronvolts opening in the Dirac spectrum, electrical resistivity remains lower than expected at low temperature and varies between devices. While subgap states are likely to play a role in this behavior, their precise nature is unclear. We present a scanning gate microscopy study of moiré superlattice devices with comparable activation energy but with different charge disorder levels. In the device with higher charge impurity (∼1010 cm-2) and lower resistivity (∼10 kΩ) at the Dirac point we observe current flow along the graphene edges. Combined with simulations, our measurements suggest that enhanced edge doping is responsible for this effect. In addition, a device with low charge impurity (∼109 cm-2) and higher resistivity (∼100 kΩ) shows subgap states in the bulk, consistent with the absence of shunting by edge currents.