For all posts "continue reading" is shown.
I deactivated all plugins, no help.
When I looked at certain posts I realized:
When I deactivated the Awesome Ad plugin (not tested with WordPress 3.4.), the plugin restored all posts to the second (a very old) version instead of the second LAST version and even left some adds inside even in the editing mode. Result
Restoring the posts was easy: I simply restore the latest Autosave or version. Thanks to the Autosave reminder, wordpress tells me that I have a very old version installed.
Still I had some issues with missing page breaks when restoring the latest version, but this issue did not show up later.