I think generally San Pedro is pretty safe. Nearly all visitors seem to feel comfortable about the level of personal safety and security on the island, from what I can tell, just as you did.
BUT, yes, incidents have happened -- over the years ... murders, rapes, muggings, knifings. And doubtless they will continue. Just like in any town of 5000 or so in the U.S. or Canada. Perhaps a bit more so in San Pedro, because the tens of thousands of "rich" tourists (certainly rich by Central American and Mexican standards) who visit are magnets for the bad guys not only in Belize but in nearby surrounding countries who are out to make an easy, fast buck. Even if the San Pedro police were highly trained and remarkably efficient, which they are not, they couldn't stop all the ways that the animals have of finding victims.
So, personally, I think that visitors should enjoy themselves realizing that it is highly unlikely they will experience any crime, but that crime does happen and to use common sense precautions just as anywhere else to give themselves the best chance of avoiding it.
Belize First Magazine http://www.turq.com/belizefirst/