Update: Seems like it had some sort of conflict with html formatting used in an HTML field on the form. (Text between <small> </small> tags). By removing this it works fine now.
Embedding a form in a post works but when I'm not logged in I can't fill in the form values. Forms embedded in pages works fine. Example: http://www.vlario.be/site/test (post) and http://www.vlario.be/site/lidmaatschap (page with is working).