Automatic washing machines are designed to dissolve the washing powder quickly into the water - so that it can begin to work as quickly as possible without leaving residues. However, factors such as the size of the wash load, the level and pressure of water entering the machine and the length of the wash cycle can all have an effect.
Some machines start by filling with water, moving the wash around in the drum and then waiting until the water reaches the right wash temperature. The powder could become trapped in the washing at this stage and so is prevented from dissolving properly.
Always ensuring that the machine is not overloaded should avoid most instances of residues. However, if it does happen, simply brush off the worst of the dried residue and then rinse or wash again.