The global/local tags issue has been debated time and again in this forum. That is how wp.com works. Period. It is possible to 'outsmart' the global tags by creating tags and categories that are unique to your blog, which means that only your posts will show up when people click them.
As TSP pointed out correctly, if you change your privacy settings, you will not be found by searches on wp.com or by searches in Google or other search engines, so that is a major drawback.
If don't want to change the privacy settings and you don't like global tags/categories, it is possible to remove them (without changing the privacy settings) using the CSS Upgrade, leaving only the sidebar category and tag widgets. However, depending on the theme, usually this also removes much or all of the post info, such as author and date, something you would want to keep.
The new INove theme has the option of not displaying the global tags and categories with the post. You will still be listed in global tags and categories, and people will find you when searching on wp.com or in Google, but in order to see related posts they will need to use your sidebar widgets. If you don't want global tags and categories, INove is your best option.