By David Rosenthal.
This old photo has that cracked texture to it, common in the 1970s. Click on the photo to see the detail better, and you'll see it's pocked with reflections of the texture that the scanner picked up.
Here's a 100% crop showing the problem we face.
Any way you cut it, you're going to lose a little detail in the shot, but we can get rid of the texture pretty successfully.
I used a technique for dealing with blemishes. Duplicate the layer, and add Gaussian Blur -- enough that it removes what you don't want. Your whole image will be really blurry now, but don't worry.
After you get that set, go to the History Palette, and select the layer just above the Blur state (in blue in this screen capture), then select the box to the left of the Blur. This sets the History Brush. In other words, it sets which history state the brush will paint with. The History Brush paints History States.
The History Brush is the paint brush with the arrow.
After darkening the white points, I was left with some dark points. Not so much of a problem in the hair and shirt, but still very distracting in the background and skin.
To take care of this, you just set your History Brush mode from Darken to Lighten. This will lighten those dark points. Keep in mind that any point that you do both Darken AND Lighten, you've basically just blurred the heck out of it, so be careful.
Here you see the final, where I've run the HIstory Brush in both Darken and Lighten modes.