Process 1 app, then its plate lunch time, then its take a break for the rest of the day
That's a hard days work.
Life is tough
But who cares
We checked the box
We are box checkers after all
Great job! Wooooo!! 
That, or maybe;
New application -- start on first page.
Missing a copy of something -- put in in the stack to contact applicant.
Missing a signature -- put in in the stack to contact applicant.
Guy who contacts applicants for missing stuff comes in on Wednesdays for half a day. Makes calls and leaves. If he's on vacation, the applications sit in his box another week or two.
Once all required forms and signatures are submitted, request background check info from HMOs, doctors, health dept, FBI, criminal records division, etc.
Now wait indefinitely until those agencies and businesses respond.
Once all responses are received, do a complete review of all paperwork. If anything needs remedying, put it in the Wednesday guy's in-box.
Once the discrepancies are corrected, do another full review, start to finish, in case you missed something in the previous reviews. If you find any "new" problems previously overlooked, it goes back into the Wednesday guy's pile.
If all is completed, send the application to the Police Chief for final review and approval/rejection. Wait indefinitely for the application to be returned.
That's what I'm envisioning anyway.