Apparently pre-rinsing confuses the dishwasher or something. Not doing it leaves me with residue all over the other dishes though π€·
Looks like there's something wrong with your dishwasher. I've had this effect once on one that couldn't heat up the water any more.
It depends a bit on what exactly the residue is you're talking about, but usually it's grease that wasn't properly picked up by the water, just redistributed among your dishes. That is usually because the dishwasher detergent did not properly activate, which in turn is usually because the water does not get hot enough. (Never mind some fats also just stay solid at room temperature.)
A properly working dishwasher does not leave any residue on your dishes.