  Van der Waals structures formed by aligning monolayer graphene with
insulating layers of hexagonal boron nitride exhibit a moir\'e superlattice
that is expected to break sublattice symmetry. Despite an energy gap of several
tens of millielectron volts 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
moir\'e superlattice devices with comparable activation energy but with
different charge disorder levels. In the device with higher charge impurity
(~${10}^{10}$ $cm^{-2}$) and lower resistivity (~$10$ $k{\Omega}$) 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 (~$10^9$
$cm^{-2}$) and higher resistivity (~$100$ $k{\Omega}$) shows subgap states in
the bulk, consistent with the absence of shunting by edge currents.
