from The American Heritage Dictionary
USAGE NOTE: It is widely asserted that none is equivalent to no one, and hence requires a singular verb and singular pronoun: None of the prisoners was given his soup. It is true that none is etymologically derived from the Old English word łn, “one,” but the word has been used as both a singular and a plural noun from Old English onward. The plural use can be found in reputable sources such as the King James Bible, Dryden, and Burke; and H.W. Fowler described the traditional rule as “a mistake.” Either a singular or a plural verb is acceptably used in a sentence such as None of the conspirators has (or have) been brought to trial. When none is modified by almost, however, it is difficult to avoid treating the word as a plural: Almost none of the officials were (not was) interviewed by the committee. None can only be plural in its use in sentences such as None but his most loyal supporters believe (not believes) his story. See Usage Note at every, neither.
In your example sentence (None of us is perfect.) I would go for 'is" because that's what I learned at school. I suppose that would make me a purist, or maybe I am just old-fashioned. We do hear the plural form a lot nowadays, though. I found the following in Betty Azar's English Grammar:
Subjects with none of are considered singular in very formal English, but plural verbs are often used in informal speech writing.