Rental laws vary widely from state to state and usually are not written to the landlord's benefit.

I think in this situation I would make sure the renter knew that unless it was extremely minor or a bona fide emergency he was not to make any changes to the house. A non-working dishwasher is not an emergency.  An inconvenience, but not an emergency.  Tell him since this apparently was not clearly understood this time is just a warning.

Then add if YOU can remove the dishwasher without damaging the house when he eventually moves (everyone eventually moves unless they die there) he can take the dishwasher with him.

If a tenant calls and you can't answer (it happens) call him back as soon as possible.  Don't let it sit and fester like you did this time

Oh, among your papers I hope you include lead disclosure

http://portal.hud.gov/hudportal/HUD?src=/program_offices/healthy_homes/enforcement/disclosure

Easier read at http://www.mrlandlord.com/lead/