All you can do is try your best to get to know the person (not just get to know ABOUT them). It has already been stated in other posts that it is a pretty common that a guy will be brought into a lodge with a petition, will be introduced by a Brother, and while everyone is having coffee the petition will be passed around, making it back to the petitioner with all the required signatures. I have even seen it happen where some of the Brothers were deep in a conversation and didn't even look up and ask the guy a question or even look over the petition.
I personally have my own standards when it comes to petitions put in front o me, whether just getting passed around like that or being assigned to an investigation committee. I won't just sign someone's petition if I don't know them. Of course, if the guy shows up week after week for coffee and a few of my Brothers vouch for him, I will consider it. But not someone that literally just walked in the door and there is some big rush to get the petition done so that it can be read that night.
When I am assigned to investigate, I kinda go against the grain of most of the Brothers in my lodge. For years, they have had the habit of ALL THREE investigators meeting with the petitioner at the same time (a lot of times just up at the lodge). I like to call him up, and meet him on my own. I like to arrange a meet at his house if at all possible. The most impotant part (in my opinion), is that I don't go down the ordered list of questions on the investigation form and petition. I ask the questions out of order. Not to try and stump him on anything, but to make it more like a personal visit and give him the feeling that I want to get to know HIM. And I also ask other things about him so that I can get to know HIM.
I also go through some other avenues to see if I can get a better picture of who he is and how well MY Fraternity will benefit from having him and if he might benefit and stick with it. Just like Bro. Lins said, I don't want to cringe at the thought of him going to another lodge saying where his home lodge is and representing us in a bad way. Or the uninitiated seeing that he is a Mason and getting a bad idea about it.
Most of all, I like to surround myself with good people. I like to get to know the petititioner as if he was also petitioning to be my friend or literally my brother lol.