  We comment on several points concerning unparticles which have been
overlooked in the literature. One regards Mack's unitarity constraint lower
bounds on CFT operator dimensions,e.g. d\geq 3 for primary, gauge invariant,
vector unparticle operators. We correct the results in the literature to
account for this, and also for a needed correction in the form of the
propagator for vector and tensor unparticles. We show that the unitarity
constraints can be directly related to unitarity requirements on scattering
amplitudes of particles, e.g. those of the standard model, coupled to the CFT
operators. We also stress the existence of explicit standard model contact
terms, which are generically induced by the coupling to the CFT (or any other
hidden sector), and are subject to LEP bounds. Barring an unknown mechanism to
tune away these contact interactions, they can swamp interference effects
generated by the CFT. We illustrate these points in the context of a weakly
coupled CFT example. A significant amount of the unparticle literature should
be reconsidered in light of the observations in this note.
