Does tetrachlorodibenzo-p-dioxin (2,3,7,8) have a nonzero dipole moment?
The best answer for this seems to be in Structure, Energy, Vibrational Frequencies, and Potential Energy Curve of
2,3,7,8-Tetrachlorinated Dibenzo-p-dioxin: Ab Initio MO Studies J. Phys. Chem., 1996, 100 (12), pp 4810–4814.  

This research finds that though planar is the lowest energy conformation, the energy for bending with respect to the O-O axis from 180 degrees to 170 degrees is only 0.008 kcal/mol.  The molecule flaps like a butterfly.  

The article says:  


  At ambient temperatures, nonplanar conformations
  will be significantly populated for this potential. This prediction
  accounts for the experimental results that the electric dipole
  moment of the DD molecules is reported to be 0.64 D. [reference 24]  


Where "DD" means the unsubstituted dioxin and where reference 24 is Higashi, K.; Uyeo, S. J. Chem. Soc. Jpn. 1941, 62, 396.