It's the encoding. If I set my browser's encoding to UTF-8 (alt-key > view > encoding > Unicode), the post comes out right with quotes and double quotes.

But I have this issue all the time. User names with umlauts are also messed up unless I specify a different encoding. But usually I have to set my browser's encoding to a different encoding again to view those correctly. I'm not enough of a web expert to tell how issues like this can be fixed permamently for all users.