Wow. That was probably one othe easiest $90 (or whatever the minimum cost for a service call is these days) that plumber ever earned. Our sink and dishwasher both had backed up a couple of weeks ago, and the handyman had snaked it out. The dishwasher backed up again on Monday, so both I and the landlord assumed it was another clog, and this time she called the plumber. Who finally got here today, I showed him into the kitchen and wandered away back to the computer. And a minute later he called me back in. Apparently the little disherwasher-overflow thing on the sink, which is apparently something called an 'air gap', had clogged. You pull the cover off, you unscrew the top of the valve by hand, and you clear it, and whoosh, the dishwasher drains.
I was vaguely embarrassed, but then I compared it to a good sysadmin: something can look horribly broken, and then they can come in, tweak one thing, and everything is right again. It's all in the knowledge.