I had the same problem when I filled out the secondary. I think I ended up putting 04/22/2006 and it worked...but I'm not sure. I remember it didn't like the word 'April.' Unfortunately, it won't let you see your completed application once you've submitted it, so I can't tell you for sure.
Also, be advised that once you click the 'submit' button, it's GONE. There's no "are you sure you want to submit your application" kind of question. So make sure you're DEFINITELY ready to submit before you hit the button!