Everywhere there are pretty pictures of failing tests shown inline in the code editor, like in Peepcodes Objective-C for Rubyist screencast and in apples own technical documentation:
When I build my test-target, all I get is a little red icon down in the right corner, stating something went wrong. When clicking on it, I get the Build Results, where I can start to hunt for test results.
Do anyone have a clue on what´s wrong?
Have a look at your Xcode preferences. Under the Building tab you want to change your settings for Message Bubbles.
This works for Xcode 3.1 which it looks like the image you've shown. Xcode 3.2 has a different style of bubble and doesn't have this preference.
Press "Cmd =" to travel between build results, you should see a warning.
Also, that specific warning seems like it's from the static analyzer - you turn that on by going to project preferences and checkmarking "run static analyzer" or by using the "Build and Analyze" option.
According to this question, this behaviour is a known bug in XCode 3.2. I do wish Apple had mentioned this somewhere though, or updated their screen shots; I got just as confused as you did.