I now made two screenshots of Mail: The first one while the external display was disconnected, the second one when it was connected (and Mail moved to the external display). I opened both screenshots in Photoshop and there was a clear difference between the font renderings: On the screenshot of the internal display, the fonts are smoothed with black and grey pixels only, while on the screenshot from the external display they are smoothed with colored pixels. This is the reason why the text looks so bad on the external one. Therefore, it is definitely a problem of the font rendering. In Photoshop, the difference of font rendering is clearly visible!
See here:
http://img208.imageshack.us/img208/5389/fontt.jpg
The first line is internal display, the second line external display. That's unbelievable.
Another thing: I found out that it's not only Mail that has the problem - it is any application that was started after the external display had been connected. It seems that OS X applies the font rendering setting at the moment a application is starts. When I disconnect the display, start Finder, Mail, Safari and so on, and then connect the display, then all the applications look great even on the external display. When I quit the apps and then restart, the font rendering is broken again