After a crop, I noticed that the whole picture is used by Lightroom when erasing details (spot removal) in the corners or the edges of a picture.
The result is that quite often there is something of the cropped section in the corrected zone. I guess that taking into account the cropped image and not the whole one would be more efficient...
To make myself clear an example attanched, the crop and the result.
I finally used the healing tool to get a satisfaying result.