Hi Aga!

You have a good eye - the white growth on the leaves is a fungal disease called powdery mildew. This is a very common disease (my dogwood has it right now!), but the infection is rarely lethal.  but does cause leaf yellowing and browning, leaf distortion, premature leaf drop and blemished or aborted flowers, and slower-than-normal growth. There is not much you can do to treat this - try to ensure the tree has adequate air circulation and some sunlight to reduce humidity levels. There are varieties of dogwood that are resistant to powdery mildew, if you end up replacing the tree in the future (they're listed on the provided link above). 

In addition, your dogwood also has a leaf spotting disease called anthracnose. It is too late to spray - they're only effective when sprayed preventatively right as leaves are coming out. You can prune out any dead wood when we have dry weather and rake and dispose of any dead leaves in the fall to prevent overwintering pathogens. Continue to monitor the tree and ensure it is properly mulched and watered to keep it healthy.

Jamie