phrenq

Sorry for the delay — it took me a bit to narrow down the key steps to reproduce.

You should be able to repro in Twenty Twelve, if you replace index.php with this file: https://gist.github.com/frankpape/44eb1fd8499394ea0988

I did this in a fresh test WordPress install, with no other plugins installed. The only content changes I made were to add some manual excerpts to the sample post and the sample page.

They key points are:
1. The sidebar with the Feature a Page Widget must be rendered before the loop.
2. The apply_filters call should happen inside the loop.

Hope that helps!