Should a fresh install of Drupal have failing tests and what to do with the failing tests?
All tests are run on every patch that is posted on drupal.org, fully automated. Nothing is commited unless all tests are passing (It happens that something is commited that breaks the tests (for example if the tests only fail sometimes or the fail was not triggered on the patch for some other reason. However, development comes to a complete halt in such cases until the tests are working again.

But, these automated tests are run on equally configured, highly tuned linux servers (they currently run all of the core tests in ~40 minutes, I'm not going to ask how many hours it took you :)).

So, what is possible is that your system is somehow configured differently, uses different version of PHP, MySQL, the OS or something else. The tests should of course pass on every supported environment, so what I would recommend is creating a core issue, list the not-working tests (including the exact failures, e.g. with screenshots) and a detailed description of your set-up including your versions of PHP, MySQL, Apache, OS, extensions and so on.

I know that DamZ does regularly run all tests on different setups, including PostgreSQL, Windows and so on and I'm pretty sure that most except the Linux/MySQL env still have known failures. Edit: The site for this is on http://drupaltesting.org/, but it looks like it's been broken (the test environment, not the tests) for a few months now..