This being a black and white photo, the
first thing I did was grayscale it.

(Sepia tone can always be added back layer as the last step. There are slicker ways to go b&w also but I copped for the easy method.)
Then I copied the background layer, and changed the blending mode to vivid light.
The smudges are going to take a lot of time and patience, but they're easier to find now I think. This photo's got a focus problem too.