  With the advent of wide-field cosmological surveys, we are approaching
samples of hundreds of thousands of galaxy clusters. While such large numbers
will help reduce statistical uncertainties, the control of systematics in
cluster masses becomes ever more crucial. Here we examine the effects of an
important source of systematic uncertainty in galaxy-based cluster mass
estimation techniques: the presence of significant dynamical substructure.
Dynamical substructure manifests as dynamically distinct subgroups in
phase-space, indicating an 'unrelaxed' state. This issue affects around a
quarter of clusters in a generally selected sample. We employ a set of mock
clusters whose masses have been measured homogeneously with commonly-used
galaxy-based mass estimation techniques (kinematic, richness, caustic, radial
methods). We use these to study how the relation between observationally
estimated and true cluster mass depends on the presence of substructure, as
identified by various popular diagnostics. We find that the scatter for an
ensemble of clusters does not increase dramatically for clusters with dynamical
substructure. However, we find a systematic bias for all methods, such that
clusters with significant substructure have higher measured masses than their
relaxed counterparts. This bias depends on cluster mass: the most massive
clusters are largely unaffected by the presence of significant substructure,
but masses are significantly overestimated for lower mass clusters, by
$\sim10\%$ at $10^{14}$ and $\geq20\%$ for $\leq10^{13.5}$. The use of cluster
samples with different levels of substructure can, therefore, bias certain
cosmological parameters up to a level comparable to the typical uncertainties
in current cosmological studies.
