Need tips for removing stains on old black and white photo

There are different kinds of damage to photos. The kind where you lose information completely, like a tear or a hole, are best fixed using the Spot Healing Brush or content-aware fill; something where we're having to replace pixel information with what's around or making it up completely. Then there are the kinds of damage where the info is still there, but its been affected in someway, like a stain or an under-developed negative. In those cases its most important to get the selection masks right for each damaged area so you are only working on portions of the image at a time. 

The best thing would be to concentrate on getting good clean selection masks of those swiped & scratched areas. More individual selection mask layers for each unique area of damage would be good to allow for more precise control later. There's no single right way to best select those areas so try a combination of different things like the Magnetic Lasso tool and Selection options. Also don't forget about things like feathering your mask selections. 

One thing that might work is using the Eyedropper tool with a large sample size selection (5 by 5 average or higher), then selecting a color that approximates the tone of the "stain". Paint in that layer mask on a new layer and then set that layers transparency to something like Difference or Divide. Here you may need to play with the layer transparency settings or try a completely different transparency style like Linear Burn or Color Burn to get the color to adjust in that damaged area to match the rest of the photo. I've used this same technique to get rid of vignetting in old photos. 

Good luck!

I'd start out with content-aware fill and see how far that can take me, then I'd bet you could copy-paste selected areas and cover the bad parts that way in certain spots.