We participate in indirect lending with several car dealerships, we get applications after the customer has come and gone from the dealership, the application is joint as evidenced from both signatures on the application and the joint acknowledgement is checked however they did not initial the joint acknowledgement, what now?

Kick it back to the dealer and don't accept it.

Agree with Randy, but rest assured that every one in the future will be initialed, (whether it be by the customer or dealer initialing with the customer's initials on behalf of the customer).

(Seen it happen - sent contract back to dealer and got it back in the next run - a half-hour later. "The customers just happened to be in the dealership and were glad to initial it.")