Well he's probably got away with it by not having an inventory.
And he's right, it's not essential to have a dishwasher, however if i was a prospective tenant and saw a dishwasher in place, then i would expect it to be working. If the LL doesn't want to replace it, then he should just remove it and stick a cupboard in it's place.
It also doesn't give a prospective tenant a good feeling if he see's broken white goods - what if something essential like the washing machine or boiler went next.
It's easy to just point those things out to anyone having a viewing.