When you are getting to know someone that you have no connection with and you have no friends who have connections with this person and you know of nobody who knows this person, you in some ways are at a disadvantage for any inside resources to figure out what this person's character is like and get valuable feedback. I believe it is still a doable situation, just like interviewing applicants for a job, you simply have to increase your scope of questions and observation and be willing to give ample time to situations and history to determine what they truly are like at their core. You have to approach it knowing that there are added dimension of challenges in getting to know someone.
So what are some ways I have done this?
In dating, if given the opportunity, meet some of their friends. See how they interact with people they already have relationships with, people they feel comfortable with, people who are interested in the friendship and well being of the person you are getting to know. Meet their boss/coworkers/employees and see how they communicate with them. Do these work family respond in fear or admiration to this person? How responsive are they to this person? What messages does their body language display as they greet the person, as they carry on a conversation and have discussions? Do they talk just about work or life too? How do they part ways? Meet some of the family. See if they are affectionate with each other (for instance give each other hugs). What do they talk about? Is the communication loving and responsive, a give and take between both parties, with a genuine interest? Are they talkative or do they run out of things to discuss? Are they polite and mannerly, or rude and mean? When you go out to eat, how does he treat the waiter or waitress? Does he get angry in traffic? What sort of things irritate him?
All these situations give opportunity for you to interact and learn about someone. These things are subtle ways to observe someone in action and tell about the type of character he has. Don't think that you are being too observant. The beginning of a relationship is critical to understanding the personality, beliefs, desires and challenges you will face if you decide to be in a relationship with this person. You can not ignore the little things because they will be big things later.
That being said, if a situation is not as you want it to be or you see signs of something that might be an issue, I say make a mental alert note of it and file it in the back of your mind and see if it happens a 2nd or 3rd time. If you see a pattern, then you potentially have something to be concerned about. If it is a one time incident that doesn't repeat itself, then you probably are safe to say that you got to see that person at a moment when they were not their best but isn't a character flaw. We all have these times and so I wouldn't rule someone out from one situation or observation, but I also wouldn't be afraid to rule someone out if the one time incident was a significant concern even if you don't see a pattern. You have to use your best judgement and decipher if the situation needs grace and love or will be something that will negatively affect a relationship.
I also say don't hesitate to ask questions if something presents itself that you are unsure about. There is nothing wrong with saying, I saw how you responded to this and I want to know if this is the typical way you react or if you were just stressed in the moment. Get that person to talk about themselves so you can learn what they think of their actions, what they view on their conduct, and how they react to you questioning them. All these things give you insight into someones heart and whether the two of you will have the ability to be in a relationship. If you can't figure out whether it is something you should be concerned about, in my experience, trust that it will show itself in some other form or fashion. The truth cannot be hid. Yes, I believe people can be deceitful and portray themselves in a way they are not, but if you are being very intentional about how you get to know this person, the fact of the matter is it will force other things to come to light.
Be observant. Stay on your toes. Don't give in to your feelings. Think things through. Discuss the situation with others to get their input. Be open to seeing the truth.