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I have an iPhone 4S, just upgraded from iPhone 4 where I had the same problem:
When I add new contacts I cannot subsequently find them in my contact list. However when on of these contacts calls me my their # is recognized and the screen will display who is calling - name, just as I had entered when adding them to my list.
I have tried to search in "all contacts" and in every contact folder.... all to no avail.
Can anyone help me out?
Much appreciated in advance.
I would try searching by doing a "Search iPhone" (which you get to by swiping left from your home screen) and see where the contact shows up. (S)he must be somewhere!

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