The dishwasher that wouldn't drain
The water just sat there after every cycle. I pulled the filter first, which was disgusting but clean enough, so the problem was further down.
The culprit was the check valve where the drain hose meets the pump: a little rubber flap stuck closed with grease. Ten minutes in warm soapy water and it flapped like new.
Lesson: the manual had a diagram of exactly this part. I found it after I was done.