Hi there, each of your posts contains two parts, the main post body and an excerpt.
For example, let's take this post: http://ainanani.wordpress.com/2013/02/15/das-andere-ende-des-dubai-creek/
You can see in screenshot that the characters are correct in the post itself, but broken in the excerpt: http://cl.ly/image/3C0S0E391o2n
So if a theme is displaying excerpts on the homepage (like Suburbia or Imbalance 2 does), and the excerpt has broken characters in it, then broken characters would be displayed on the homepage. If a theme is using full post texts or there are no excerpts set, then the characters will display correctly.
And the same problem also exists in new posts that I produced within the wordpress system.
I checked the four most recent posts you created on http://ainanani.wordpress.com/ since migrating here and did not find broken characters. Could you please point me to them?
I had corrected the corrupt umlaute by hand after importing from posterous.
Since you originally imported from Posterous, we communicated the broken characters issue to them and they fixed it on their end (the Posterous backup files already contained broken characters). At this point, it is probably easiest not to re-import, but rather go through your posts one-by-one and deleting the excerpts with broken characters in them. If you do that, themes like Suburbia would you your full posts to generate excerpts for the frontpage, and display correct German characters.
Let me know if you need further assistance with this -- I'll be happy to go through and clean up the excerpts for you.