Remember when dealing with department staff to be courteous, cooperative and most of all curious.
Treating the customer service staff with mutal respect will go a long way toward getting your submittal processed in a timely manner.
Do not assume anything is taken care of. Ask lots of questions and make sure you get a time committment for completion of your review and approval of the application.
Make sure you leave with all your questions answered about the process and the time lines. Find out where the biggest roadblocks are. Which departments take the longest to finish the review.
Is there a way to pay overtime to speed up the process. If so, what is the procedure for making this happen on your project.