  I point out two of the subtleties referred to in the title. The first is that
gauge-invariant magnetic systems may realized under general circumstances, as
suggested by a simple theorem. The second subtlety is that care is needed to
identify the field theory simulated by a cold-atomic lattice gauge system.
Though the simplest such model confines in 2+1 dimensions, it has
non-relativistic ``gluon" excitations. Time-reversal invariance is
spontaneously broken in this system. The confinement mechanism is related to an
extra U(1) gauge invariance.There is a model, suggested long ago by D. Rohlich
and me, which is known to have relativistic spin waves. One of the outstanding
theoretical problems is a better determination of the energy-momentum relation
of spin waves in different magnetic gauge systems.
