I'll suggest a somewhat toned down version of this. In what you describe, the person who finds the placebo wand discovers a number of important things besides just that there's a wand in that location. They discover what *kind* of wand and the wand's name, so that if they see someone else using it then they know where that person got it.

Instead, I propose that when someone looks in a container (or kills a mob) that *can* contain a wand they get an echo like, "You detect a residual aura of magic about this place", or for mobs, "You detect a residual aura of magic about this sacrifice" (when they sacrifice the corpse). These echos could be made contingent on the person having "detect magic" up, granting even further utility to the detect magic spell.