The first case is when I've got a neat idea but I don't know how to implement it.
Assuming the neat idea is one that produces tangible results, write a functional test that invokes the "neat idea" code and makes some assertions about the results. Functional tests are good when you're making a cold start on an idea. They help you get started working from the outside in.
I sometimes start with a (functional) WWW::Mechanize test that invokes a CGI that doesn't exist yet, and makes some assertions about what the result looks like. Then I work inwards towards things that I can unit test. Often though, having a set of functional tests is sufficient.
Sometime if I find myself coding too far ahead, I'll stop and comment out the code I've just written. Then I'll write tests that give me a legitimate excuse to uncomment it bit by bit. It's not rare to discover that I've written stuff I don't really need. And occasionly, as you mention, a test will pass when it isn't expected to. Those end up being great opportunities for learning.
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