Question

At the beginning of a distillation procedure, why should a distilling flask be filled to not more than two-thirds its capacity?

Answer 1

To avoid the risk of the contents, product and impurities, bubbling up and over into the condenser which is intended to only take vapour of the product. You also need  to have room for the heat expansion of the liquid and the forming vapours.

You should also consider that a liquid will increase in volume when heated and leaving a flask no more than 2/3 full allows room for expansion.  if the flask were too full, there would be too little surface area for rapid evaporation and therefore the distillation would be very slow.

Hope this helps