Food trapped in big gap after a crown put in. Dentist said nothing wrong with it. (photo)

My question is did this occur during the temporary phase? If it occurred right after the crown was placed then most likely the contact between the teeth is the problem. The space that you show in your picture is normal when gum recession has taken place. Closing that space is not possible with a crown. If your floss slides through the contact with no resistance then either the crown was delivered that way or the tooth has moved. Until you and your dentist resolve this issue try Gum Brand "Soft Piks" for cleaning. These work very well.  

Hi:Food traps between teeth can lead to gum inflamation and bone loss.  I would get a second opinion on the crown as soon as possible.  Best,Dr. Maddahi

The photo before and after look like a nice job. If you did not have food getting trapped when the crowns were delivered, than there might be a cause why you are getting space. You should consult with your dentist for clenching or any other para-habits you might have that is causing the teeth to move.
Hope it helps!