  We use morphological measurements and the scatter of clusters about observed
and simulated scaling relations to examine the impact of merging and
core-related phenomena on the structure of galaxy clusters. All relations
constructed from emission-weighted mean temperature and intracluster medium
mass, X-ray luminosity, isophotal size, or near-IR luminosity show a separation
between cool core (CC) and non-cool core (NCC) clusters. We attribute this
partially to a temperature bias in CC clusters, and partially to other cool
core-related structural changes. We attempt to minimize CC/NCC separation in
scaling relations by applying a uniform scale factor to CC cluster temperatures
and determining the scale factor for each relation that minimizes the
separation between CC and NCC populations, and by introducing central surface
brightness as a third parameter in relations. The latter approach reduces
scatter in relations more than temperature scaling. We compare the scatter
within subsamples split by CC/NCC and morphological merger indicators. CC
clusters and clusters with less substructure generally exhibit higher scatter
about relations. The larger structural variations in CC clusters exit well
outside the core, suggesting that a process more global than core radiative
instability is at work. Simulations without cooling mechanisms also show no
correlation between substructure and larger scatter about relations, indicating
that any merger-related scatter increases are subtle. The results indicate that
cool core related phenomena, not merging processes, are the primary contributor
to scatter in scaling relations. Our analysis does not appear to support the
scenario in which clusters evolve cool cores over time unless they experience
major mergers. (Abridged)
