This may be surprising, but you don't actually need to rinse off dish soap. Hell, at home we don't even dry thing up, just leave them to drain and evaporate. Never noticed any kind of residue or flavour.
I just wipe it off with a wet paper towel. I never notice any residue or flavor doing that. I figure if I'm not tasting the vinegar I spray on after, I'm definitely not tasting some dish soap.
I also use a very light natural dish soap. YMMV if you're using one with strongs scents/chemicals.
