Sand and/or skim coat as needed. Keep the paper covering as intact as possible. Avoid sanding through the paper even if that means having to use more skim coating or primer.
If drywall is installed inside out then more overlapping paper edges will be seen. This is another example where more skim coating will save having to damage the paper all the way around each panel.
Note that if you put in a drywall screw so deep as to cut most of its way all around the paper, that screw has lost its holding power and does not count towards the number of screws per foot needed. While it is not possible to avoid tearing the paper directly under the screw head, the hanging chad must still be attached to the rest of the paper and held down by the screw.
When cleaning anything including baby diapers, it is better to sweep off or scrape off as much solid and semisolid material as you can first. (1) Less cleaning fluid or detergent needs to be used, (2) Less of a mushy mess which in turn means that bleaches or disinfectants will be more effective.