First, I would not use either of the methods that you tried for interpolation. I would recommend using the topogrid model (Topo to raster tool). The artifacts you are observing are most likely the result of commission errors in the classification algorithm. Without running a new algorithm you are limited to operating on the resulting raster. You can identify local "peaks" and "craters" using a defined local neighborhood if/else statement in Workstation ArcInfo/Grid. You can then smooth your dem conditional on the identified peaks. Because of the lack of docell and neighborhood notation, I am not aware of a way to conduct this analysis in ArcMap/Spatial Analyst. If anybody on the list knows I would love to hear because I have been trying to figure out how to apply docell functions within the ArcGis environment without falling back on Python. Here is the if/else statement for grid:
SETWINDOW dem
SETCELL dem
IF ( dem(0,0) > dem(-2,-2) &&~
dem(0,0) > dem(-1,-2) &&~
dem(0,0) > dem(0,-2) &&~
dem(0,0) > dem(1,-2) &&~
dem(0,0) > dem(2,-2) &&~
dem(0,0) > dem(2,-1 ) &&~
dem(0,0) > dem(2,0) &&~
dem(0,0) > dem(2,1) &&~
dem(0,0) > dem(2,2) &&~
dem(0,0) > dem(1,2) &&~
dem(0,0) > dem(0,2) &&~
dem(0,0) > dem(-1,2) &&~
dem(0,0) > dem(-2,2 ) &&~
dem(0,0) > dem(-2,1) &&~
dem(0,0) > dem(-2,0) &&~
dem(0,0) > dem(-2,-1) ) peaks = 1
ELSE IF ( dem(0,0) < dem(-1,-1) &&~
dem(0,0) < dem(0,-1) &&~
dem(0,0) < dem(1,-1) &&~
dem(0,0) < dem(-1,0) &&~
dem(0,0) < dem(-1,1) &&~
dem(0,0) < dem(0,1 ) &&~
dem(0,0) < dem(1,1) &&~
dem(0,0) < dem(1,0) ) peaks = 1
ELSE peaks = 0
ENDIF
You can then apply a conditional focal function to smooth only the pixels associated with peaks/craters.
newdem = CON(peaks == 1, focalmean(dem), dem)
An alternative may be the fill command in grid using the peak option. Looking at the ArcMap version I do not immediately see the peak option.
"PEAK - all peaks less than the {z_limit} higher than their highest adjacent neighbor will be cut down to the height of that neighbor. A peak is a cell where no adjacent cells are higher."