First, use a magnet to find any ferrous surfaces on your dishwasher. Even if your dishwasher appears to be plastic, there may be metal bracing in some areas. If the magnet sticks, you are in business.
Put two magnets in an Altoids tin, with one on the lid and one on the bottom. This way, the tin will stick to your washer no matter which side is facing out.
Finally, put nametags (or other adhesive labels) reading “Clean” and “Dirty” on opposite sides. Flip the indicator as needed.