I think I've found what's been causing that bad taste I've been getting lately. It wasn't, as I thought, accidental transfer of Icy Hot or Tiger Balm. It's the box of Cascade. Last time I bought some I couldn't find my usual blend, so I bought some with bleach and 'Fresh Rapids Scent.'
I needed a while to locate the source because my dishwasher has graduated cups. You're supposed to fill them proportionately to how dirty the load is. Last load I had some pretty greasy stuff and filled the cups. The result was a terrible taste on everything washed, particularly the plastic tumblers I use.
I ran the dishes still in the washer through a hot rinse cycle, and manually rinsed some stuff I'd already put away. The taste is gone.