it seems like whether he does her dishes is between the two of them; more related to how he can pay her back for extending upon her resources (which she may or may not care about)...ultimately, her dirty dishes are *her* responsibility, whether she does them herself or makes arrangements for someone else to do it for her.
i think you can bring up the point that the rental arrangement has changed without your consent. assuming that you three split the cost of the home in total, it is unfair for one party to introduce an unpaying tenant into the mix, using resources (space, electricity, cable) that you are not compensated for. maybe have a household meeting where you talk about how this guy can either leave, or begin paying a quarter of rent and expenses.