Is the range of this plot correct using *ScalingFunctions -> "Log"*?

If I correctly understand it, you want to build a log-plot of a fuction taking negative values. In this case the ScalingFunctions -> "Log" option does not do the job. This can be done as follows. Compare

DiscretePlot[(-1)^n*n!, {n, 2, 7}, PlotRange -> All]

with

DiscretePlot[Piecewise[{{Log[Max[(-1)^n*n!, 0]], (-1)^n*n! >= 
 0}, {-Log[-Min[(-1)^n*n!, 0]], (-1)^n*n! < 0}}], {n, 2, 7}]