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Sorry, but I still think your judgement call was flawed. Obviously we won't agree on this point. I just hope one of your neighbors didn't pay the price for your apathy.

No need to get snippy over it. You may think you'd be wasting your day contacting the police over it, but you have no idea what chain of events could have taken place because you didn't.
Someone usually has to be way out of their way to be in your backyard. I've noticed most of the backyards in the suburbs here in Houston are fenced. Even without a fence, its customary to knock at someone's front door.
You choose to up the ante by threatening armed response (TPC 9.04). Well within your right to do so, IMHO, INAL, YMMV.
I'm sorry, but IMHO it is irresponsible to not notify the police in such a scenerio.
Worst case, he shuffled down the street and commited a heinous crime. I could not live with myself if I allowed that to happen.

http://record-eagle.com/local/x10485128 ... -in-attack" onclick="window.open(this.href);return false;

http://www.kcra.com/r/21240028/detail.html" onclick="window.open(this.href);return false;

http://www.pennlive.com/midstate/index. ... _rape.html" onclick="window.open(this.href);return false;

http://www.wate.com/Global/story.asp?S=13309838" onclick="window.open(this.href);return false;

Sorry, but not calling the police was a no-no.
What if 5 minutes later he breaks into someone's house down the street? What if some mom is home and he harms her? Maybe he likes making house-wife-skin-clothes. Just becuase he looked harmless, doesn't mean that he was. You felt threatened enough to show him your gun, afterall.
Aside from that, what if Mr. homeless guy was just lost, and had a legitimate reason? Say, one of your neighbors invited him over for some food. Okay, he doesn't have a legitimate reason to be at your house, but follow me. So, he gets a little lost and is knocking at your door. You (rightly) scare the bejesus out of him. He calls the police. You have no idea what his story to the police might be.
Just food for thought.