Some know me better than I know myself. I'll have my best friends point out to me flaws that I had never noticed. I sometimes get defensive and deny it. I later know that they were just trying to help, but it was completely true. I'm not saying that every person can be really understood, but some of us are just open books sometimes. I think the only reason it may be hard to know other people is because people are constantly changing their minds, so they don't even know themselves.
I agree with SecretSoleil's comments. We seem to always reserve the right to surprise and astonish others and ourselves. I think I would even go as far as answering in the negative the question 'is it possible to know to know ourselves?'.
The reason I hold this stance is based on many factors, primarily that we are always in the process of becoming, life is change, constant change, that includes us, our biological and psychological development included. The second reason would have something to do with the fact that a great percentage of what is happening in our brains is taking place below the radar, out of the scope of our conscious awareness. The third reason (and there's a fourth and a fifth and a sixth and more but I shan't bore you all to death with those, lol!) would be linked to the dynamic nature of our responses to the world and those we meet, we do not respond in isolation or a vacuum, responses are elicited by very specific sets of circumstances in very specific contexts, these are not always predictable or within the limits of what we know of ourselves and those we are interacting with - a comfort zone of sorts, if you will - and therein hides the element of surprise, just waiting to leap and catch you unawares :)
We are such an interesting species, don't you think? That we can even ponder these things never ceases to amaze me.
I said NO. From what I have observed from talk shows and/or news, people are constantly surprised to discover someone they thought they knew well for many years could end up accomplishing some terrible act. People are more than capable of effectively hiding their inner 'demons,' so to speak. Our brains are very amazing and intricate. This is an excellent question.