How to darken / heal bright spots while retaining texture

[denzjos]

try this : 
open the picture
copy the layer
blur 2 to the copy layer 
copy the blurred layer (layer 2) 
on layer 2 : filters / enhance / high pass (if not, reset to standard values :  4.0 / 1.000)
on layer 2 : colours / brightness-contrast (set contrast 15 / brightness 0)
on layer 2 : set layer mode to linear light 
in needed, use filters / enhance / sharpen (unsharp mask)
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An easy way to get rid of the white points, use Qmic Qt :

Artistic / Kuwahara (Iritations 2 / Radius 2)
or
Artistic / Sharp Abstract (Spatial scale 2.4)
or
Repair / Recursive Median (Median radius 4 / Repeats 2)
or
Repair / Remove hot pixels (Mask size 4 / Threshold 10)