Trust me I understand all too well about toxic parents who lose their temper over every little thing. Unacceptable

But I honestly would totally lose it if I got home from work and there was bowl from breakfast still unwashed by the sink (all day?). And a dirty dish on a coffee table (why on coffee table?) (and why is it left there?) from supper. I'd would be so very not ok (unless whoever kept eating and leaving their dirty dishes was incapacitated such as elderly or perhaps recovering from chemo session or something else drastic). And I have huge pet peeve about "I didn't know if dishes were clean or dirty". Why don't they know? Don't they live there? I understand it's dad's job to empty dishwasher (why it's his job though?) but I'd personally would expect those tasks to get done by whoever is home, not at work all day.

Again your father needs to remain civil. Yelling and screaming is not the way to go about. Maybe there is a need for family meeting about chores and civil behavior (although I know my dad wouldn't accept responsibility, yours might be the same).