They look like specks of mould on the petals of the dying-off flowers. The higher up flowers look OK - presumably they're opening later than the lower ones. I don't think there's anything you can or should do - nothing lasts forever, except plastic flowers.

This looks like Downy mildew, pale areas on upper leaf with gray/white even purplish patches underneath. We have had odd periods of cool/wet nights/and now warm humid days this year making it much worse.
From your picture I wnder if its an enclosed space? Delphiniums need space between them to encourage good air circulation and only water the soil to keep the foliage dry. If you have a really heavily affected plant its best to gee rid?