If your washer isn't clean, you can't expect what you put into it to come out clean either. Dirt finds a way into the washing machine, especially with kids around, and it doesn't leave. Cleaning these streaks and stains is easily accomplished with a little time and bleach.
Turn on the washing machine and allow it to fill up with hot water.
Add 474 ml (2 cups) of bleach.
Turn off the machine and allow the bleach and water to soak in the barrel for an hour.
Turn the machine on and allow it to run through a full cycle. The washing machine will rinse away all of the bleach on its own.
Dry the inside of the barrel with a clean, dry towel.
Add 200 g (1 cup) of baking soda to the washing machine with the bleach for an even better cleaning job. Vinegar is an environmentally safe alternative to bleach.