  We construct a continuum model of twisted trilayer graphene using {\it ab
initio} density-functional-theory calculations, and apply it to address twisted
trilayer electronic structure. Our model accounts for moir\'e variation in site
energies, hopping between outside layers and within layers. We focus on the
role of a mirror symmetry present in ABA graphene trilayers with a middle layer
twist. The mirror symmetry is lost intentionally when a displacement field is
applied between layers, and unintentionally when the top layer is shifted
laterally relative to the bottom layer. We use two band structure
characteristics that are directly relevant to transport measurements, the Drude
weight and the weak-field Hall conductivity, and relate them via the Hall
density to assess the influence of the accidental lateral stacking shifts
currently present in all experimental devices on electronic properties, and
comment on the role of the possible importance of accidental lateral stacking
shifts for superconductivity in twisted trilayers.
