As dV8 pointed out, there are several problems in addition to the bright speckles. I'll only deal with the speckles and describe an automated 1st pass to minimize their effect.
1) Using any combination of "find edges", brushes and any other tool that you like, make a mask that identifies the edges (areas that should receive no treatment). It should look something like this:
2) Duplicate the original onto a new layer, set its blending mode to "darken", and add a layer mask that is the inverse of the edge mask you just developed.
3) Run PS's "Dust and Scratches" filter on that layer. Start with the radius around 5 px, and the threshold around 40, and adjust to your own preferences.
4) At this point, you are essentially done.
5) Of course, you can do things like reduce the opacity of this layer to reduce the effect or adjust the opacity of the mask to fine tune the edge effect. You can also modify the mask on a pixel-by-pixel basis by painting in white, black, or anything in-between to deal with troublesome pixels. Most of these typically occur around sharp edges. From there you can attack some of the other problems present in the original.
What I obtained is shown below. Total time about 5 minutes, most of which was spend writing up this post, LOL.
Of course, by far, the best way to deal with this problem is to recognize what causes it and prevent it from happening in the first place.
The cause of problems like this is an uneven surface on the print, some areas of which specularly reflects light from the scanner's bulb right into the CCD array. You've got a couple of choices:
a) If you are good at photography and have the right equipment, instead of scanning, you should rephotograph the print with polarizing gels over each of your lights, and a conventional polarizing filter in front of your lens with its axis 90 degrees to the axes of the filters on the lights. This is the way museums get good quality reproductions of artwork with thick reflective impasto layers or other sources of glint (eg, mixed media with embedded pieces of glass or plastic).
b) If you don't want to get into re-photographing it, re-scan the print several times, changing the angle that the print is laying on the scanner dramatically and randomly between scans. Accurately straighten out and re-position the scans in PS and overlay them. Set the blending mode of each layer above the first to "darken", or put them into a stack with the operation set to "Minimum". This way, the final result for each pixel is always produced by the least reflective orientation of the scan.
Done correctly, either of these methods will be vastly superior to the "dust and scratches" method that I described at the beginning of this post.
HTH,
Tom M