The bits will be a combination of broken down food debris and particles of limescale. They will have been baked on hard during the drying cycle leaving the crocks dirty.
Try to rinse off any big lumps of food before loading the machine but above all use a good quality rinse aid - avoid the multi-tabs.
The dirt is picked up by the rinsing water - rinse aid helps the rinsing water to drain off before the drying cycle - poor quality or no rinse aid has the effect of leaving the rinse water still on the crockery to dry.
Good luck...
Peccavi, May 2010