  Noncommutative IR singularities and UV/IR mixing in relation with the
Goldstone theorem for complex scalar field theory are investigated. The
classical model has two coupling constants, $\lambda_1$ and $\lambda_2$,
associated to the two noncommutative extensions
$\phi^*\star\phi\star\phi^*\star\phi$ and $\phi^*\star\phi^*\star\phi\star\phi$
of the interaction term $|\phi|^4$ on commutative spacetime. It is shown that
the symmetric phase is one-loop renormalizable for all $\lambda_1$ and
$\lambda_2$ compatible with perturbation theory, whereas the broken phase is
proved to exist at one loop only if $\lambda_2=0$, a condition required by the
Ward identities for global U(1) invariance. Explicit expressions for the
noncommutative IR singularities in the 1PI Green functions of both phases are
given. They show that UV/IR duality does not hold for any of the phases and
that the broken phase is free of quadratic noncommutative IR singularities.
More remarkably, the pion selfenergy does not have noncommutative IR
singularities at all, which proves essential to formulate the Goldstone theorem
at one loop for all values of the spacetime noncommutativity parameter
$\theta$.
