Violation of unitarity for noncommutative field theory on compact space-tim
es is considered. Although such theories are free of ultraviolet divergence
s they still violate unitarity, while in a usual field theory such a violat
ion occurs when the theory is nonrenormalizable. The compactness of spaceli
ke coordinates implies discreteness of the time variable which leads to the
appearance of unphysical modes and violation of unitarity even in the abse
nce of a star-product in the interaction terms. Thus, this conclusion holds
also for other quantum field theories with discrete time. Violation of cau
sality., among others, occurs also in the case of the nonvanishing of the c
ommutation relations between observables at space-like distances with a typ
ical scale of noncommutativity. While this feature allows for a possible vi
olation of the spin-statistics theorem, such a violation does not rescue th
e situation but makes causality violation scale as the inverse of the mass
appearing in the considered model, i.e., it becomes even more severe. We al
so stress the role of smearing over the noncommutative coordinates entering
the field operator symbols.