'This is a not uncommon mistake.' 'This is not an uncommon mistake.' Are those sentences above both means 'This is somewhat common mistake.' ? or could they have different meanings?
This is a way of saying that "it" could be described as common or of average frequency/supply, but that the only thing they can say with confidence is that the the frequency at which something occurs, or the amount of something that exists, is not below average.
These statements have to do with the fact that its not so black and white. Things are not all either common or uncommon. Sometimes the amount of something is not notable at all (it is not oddly plentiful or oddly rare). Common generally means notably more than average, uncommon generally means notably less than average. The averages in question are usually largely contextual. And, of course, things can only be common or uncommon relative to their rarity in other areas.
It's a way of saying "I wouldn't say they are common, but I definitely would not say they're notably infrequent or rare". Another way of saying it: "you might regard the mistake as common, but I don't feel that safe calling it common. I would not call it uncommon, either, however."
Hes basically saying "the frequency with which it occurs is not noteworthy to me" or that he does not know much about the frequency, but that he does feel he knows enough to say that it would not generally be perceived as being uncommon. He does not personally think of it as particularly rare OR abundant (either because he thinks its average or because he simply doesnt know enough about it) but he believes it wouldn't be too much of a stretch to call it common.