can you let him help you with the dishes? maybe he can put some spoons in or some plastic dishes? they don't have to be in the right place, you can rearrange later, but if he gets to help a little bit then he might feel validated and not feel like the "stay away from the dishwasher" rule is arbitrary. i don't know if this would work for him or not. it works great for my dd who's a little bit older than your ds. (she'll be 3 in feb.) she's been helping on occasion probably since she was your ds's age. she usually gets bored and moves on to something else, but if she wants to help i'm happy to let her and hope i'm planting some seeds for her to continue to want to help when she's older and can really clean up after herself.
i think explaining why is very important, too. it is for us at least. if there's something i don't want her to do i'm always sure to say why, i.e.: "because if you drop a glass it breaks and makes sharp pieces we could get cut on and we have to clean it up." we've dropped a few glasses in dd's short lifetime so she's pretty familiar with it and is sad to be missing some of her faves and also hates the vacuum when we clean up. (we usually sweep except for broken glass or other really big messes.)
so, if you don't want to go the route of letting him help you, then i'd be sure to explain why you don't want him to -- "i don't want you to get hurt on the sharp knives. i don't want you to climb in the dishwasher -- that might break it," etc. and i think britishmum's advice is right on the money, too, if neither of the above work for you. just do it when daddy is around to entertain ds or after ds is napping or asleep for the night.
as far as other situations, i have to stop and ask myself, is this something that i'm making an arbitrary rule about or is this something that dd really needs to understand not to do? i think when i set up too many arbitrary rules without good reasons behind them then dd can sense that and doesn't listen when i really need her to like in issues of safety like britishmum mentioned. some things aren't really issues of safety -- like we don't draw with crayons on the wall, but i explain that it's hard to clean it off and that seems to satisfy her and, of course, i tell her that paper is the appropriate place to draw and offer her some. i guess we don't really have too many "rules" in our house, but take each situation as it comes up. sometimes that results in messes if dd is helping me in the kitchen for example, but she's washable!!