In Akonyl's (and partially manga's) case, for example, you could simply make an easy contract with those rules:
- Used tableware must not be located anywhere but the dishwasher in [insert rooms you both share], if violated, the offender suffers a fine of [amount] per piece.
- Used tableware must not be put in the dishwasher if any tableware piece of its last running is still left inside, if violated, the offender suffers a fine of [amount] per piece.
- These rules apply only if the offender is not present1.
- The fines have to be paid until the following [Monday/first day of month/whatever].
1 Optionally, you could insert a line like "and has not been present for [amount] minutes" here; otherwise, if you leave the tableware in the kitchen in order to answer the door, you violate the rules above
This allows the person you're living with (assuming the case you described with the half-emptied dishwasher applies) to either keep his used tableware in his room(s) or take your stuff out2 and put them in the dishwasher or to wash them by hand or to pay the fine. I'm not aware of the laws concerning contracts in the US, but a contract like this shouldn't really be a problem. Also, in order to count the offences, I suggest you use post-its with date and time (preventing reuse), number of items (preventing adding items (one post-it per item would need a lot of them)) and your signature (preventing fakes) to mark offending tableware you've already counted (it shouldn't really be in his interest to remove those stickers, as this means they get counted again :x).
While I doubt that that'd be the case, should he accuse you of faking numbers, you could also take photos of the tableware as proof.
2 If you are offended should he just take them out and not put them into the cupboard, you might need a definition of "emptying the dishwasher" here
