I provide a fairly systematic analysis of when quantities that are variant under a dynamical symmetry transformation should be regarded as unobservable, or redundant, or unreal; of when models related by a dynamical symmetry transformation represent the same state of affairs; and of when mathematical structure that is variant under a dynamical symmetry transformation should be regarded as surplus. In most of these cases the answer is `it depends': depends, that is, on the details of the symmetry in question. A (...) central feature of the analysis is that in order to draw any of these conclusions for a dynamical symmetry it needs to be understood in terms of its possible extensions to other physical systems, in particular to measurement devices. (shrink)