I'm reading a history of Venice right now and it's already mentioned several thefts of saints' bodies. So far, these are the thefts mentioned:
All of that fell between 800 CE and 1200 CE.
How common was this sort of theft of saintly relics? How did people view these thefts at the time?
"From the reign of Charles the Great until the age of the crusades, we have nearly one hundred relic theft accounts... Far from condemning [the thefts] as aberrations or as sins against fellow Christians from whom the saints were stolen, most people apparently praised them as true works of Christian virtue." - from "Furta Sacra - Thefts of Relics in the Central Middle Ages" by Patrick J. Geary.
These recorded accounts are representative of many, many more relic thefts. There was a good market for stolen relics, as you needed a good relic for your church or pilgrimage destination to drive customer traffic.
If there were three skulls of Saint Somebody in circulation, how could you be sure yours was the legitimate one? You knew your relic was valid if it worked miracles.
Were there moral/ethical issues in receiving "hot" relics? No - you didn't lose sleep over buying stolen merchandise since the saint wouldn't have allowed the theft of his or her relic if you weren't meant to have it!