The grit will mainly be broken down food debris - stuff you put in with the dishes - left on the crockery in the rinsing water.
Clean off the dishes before loading - and use a good quality liquid rinse aid - it helps the rinse water to drain off.
Avoid if you can the multi-tablets - use separate salt - detergent and rinse aid .
Consider a dishwasher cleaning product every now and again.
Good luck..., December 2014