  We study uniquely ergodic dynamical systems over locally compact,
sigma-compact Abelian groups. We characterize uniform convergence in
Wiener/Wintner type ergodic theorems in terms of continuity of the limit. Our
results generalize and unify earlier results of Robinson and Assani
respectively. We then turn to diffraction of quasicrystals and show how the
Bragg peaks can be calculated via a Wiener/Wintner type result. Combining these
results we prove a version of what is sometimes known as Bombieri/Taylor
conjecture. Finally, we discuss various examples including deformed model sets,
percolation models, random displacement models, and linearly repetitive
systems.
