I didn't use 'an', because a.) I didn't think to, because b.) it doesn't convey the meaning I wanted; it is not very likely that someone using a dishwasher in a home does not also own the dishwasher; and the disaster in a home would be emotionally worse than in, say, a restaurant.
Well, I never thought of or knew of woe betide meaning swift punishment, but I would consider having to clean up the resultant mess a punishment for being so sophomoric (hi, anchita) as to use dishwashing liquid in a dishwasher.