What an interesting concept.
I googled "people peculiarities" and got quite a list:
<a href="http://www.google.com/search?sourceid=navclient&ie=UTF-8&q=people peculiarities" target="_new">peculiarities</a>
I see peculiarities as falling under characteristics, as in, "he sure is a peculiar (or eccentric, melancholy, happy, interesting, weird, strange) character.
A character (where char is a human being, for chars can be weather, objects, animals) has attributes, personality traits.
Peculiar to my mind specifically means abnormal, unusual, different from the norm. Whatever normal is, that is, within the context of the story.
There are many ideas in that link I gave you. I find some Spanish personality peculiar, which for them are the order of the day.
I like to observe people. Crowded public places offer a plethora of strange characteristics, because people feel that in a crowd no one notices them picking their nose, staring at a womans's butt for an hour straight, frowning to the air in front of them, screaming personal info like phone and credit card numbers into cell phones, slips snowing down south, unmatched socks (I may be guilty), wild gestures.
Which reminds me. A while back I was practicing my Spanish on a hike. I was mouthing the words in a pretend conversation, and was gesturing to the imaginary boy I was talking to. A guy came up from behind and said, "Hi..." with raised eyebrows. My "Practicing Spanish" comment delivered me from peculiar status, I fear.
These are physical, external peculiarities. As authors and gods of our stories, we see the peculiarities inside their heads and hearts. Now it gets juicy.
Good luck.