Subtleties of Non-Abelian Gauge Theories in Cold-Atomic Lattices

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.