There are misunderstandings about the depth and scope of the statistics provided, in the Stats displays. Some blog owners are keeping logs, or maybe spreadsheets, from the numbers - and are adding up the numbers displayed, by rows and columns. Having added up the numbers, they are finding discrepancies.
My 'All Time' Stats are inconsistent with 'Monthly' Stats!and
Stats doesn't include all countries in "All Time" views!!
For any given time period, you'll find total counts for that period available on the "Overview" display.
For that same time period, you can go to the "Audience" display, and observe the 10 most active / popular Browsers, Countries, and Operating Systems. Most blogs, if they don't have a very regionalised audience, will have traffic from more than 10 countries during any time period of any length. If you add up the counts for the 10 most active countries, it's highly unlikely that the number will add up, exactly, to the total from "Overview".
Similarly, in a mature blog with any interesting number of posts, it's not terribly likely that the same 10 posts will be consistently featured during all different time periods. Posts published during this week won't yield the same "all time" activity as posts published during 2010. Each week, you should expect to see posts published during that week - or maybe the previous week - showing with more activity than older posts, during that period. Yet the older posts, having been around longer, will show more overall activity.
Additionally, we must remember that posts activity will never account for all activity in the blog. Archive retrievals, label searches, and main page views also count in the Audience, Overview, and Traffic Sources pageview totals. Even with a new blog - with less than 10 posts - you'll never get the individual posts pageview counts to add up to the audience, overview, or traffic sources pageview counts.
Stats is a good tool to highlight trends - and provides statistics that you simply won't get from other visitor logs or meters. Used properly, you'll be able to observe areas of activity - and areas where improvement is needed. Observing the techniques used in the more popular posts, and during the more active periods, you can see which techniques you can apply to the less popular posts, and try for improvement overall.
Stats will never provide a complete picture, of all visitor activity. If you want complete statistics, you're going to have to make them yourself, based upon visitor logs or meters, like FlagCounter, SiteMeter, and StatCounter. Or, instead of obsessing with the details, why not spend more time working on the blog, and improving what is needed? More publishing, less worrying.