I would say it depends. I often find things I don't like about people as I know them longer, but it isn't always something that would make them untrustworthy, and i guess they would say the same about etting to know me. There are some problems that i can't deal with and others i can tolerate and that's just how it is. Then there are the people who prove themselves untrustworthy in some issues, and those that are completely untrustworthy, and those I don't deal with anymore. Cut off and goodbye.
Those who are untrustworthy in some contexts include some family members who I see a lot of good in, but they just can't handle certain things. I no longer have them in the "need to know" listings of certain parts of my life, but I maintain contact with them for other reasons.
So, "Normal"? I think it is a natural part of learning to know people. Some will turn out to be good friends, others will not. HUGGSS