Smart automated testing sounds amazing, until you realize that it's not smart at all. The dumb computer that you're ordering to do your bidding is the same dumb computer that is going to be running your tests, and chances are the programmer is invariant as well. In short, good programmers need unit tests less and bad programmers will write bad tests. You can't fix a personnel problem with technology.
Exactly. The computer will just repeat what you tell it to do. There is the chance that you will tell it wrong (a bug in your test code), and the chance that what you told it is not true anymore. An automated test basically saves you the work of doing the same thing over an over again as you develop.
But we must keep in mind that maintaining test code has a cost. Automated testing is not a holy grail and it isn't useful 100% of the time. You should carefully decide what code is worth testing via automation.
Unit tests in general don't catch any regressions, they only help you develop.
Functional tests might be useful, but only if you are testing something that is not likely to change much. E.g.: It is not worth to automate testing the UI if you are going to completely redesign it next month.
Manual testing can actually be cheaper than maintaining test code.
