Sweet Dud is a response used to show complete an utter contempt for whatever anyone else throws at you. Whether it's critically important, or silly in nature, Sweet Dud is an appropriate response for all.
You can add dripping contempt by including contemptuous facial expressions (e.g. raise the eyebrows slightly, throw in a smirk, and quasi-chuckle), extending your arm 90 degrees from your body, and extending your hand at 45 degrees.
Jimmy: But Cindy, you can't leave me. I love you.
Cindy: Sweet Dud
Doctor: I NEED that Scalpel, or this patient is going to die!
Nurse: Sweet Dud
Amanda: *inaudible garbage*
Scott: What was that?
Amanda: I said I was...
Scott: Sweet Dud