Our city has them done in about 3-5 days, half the information on the permit I leave blank. Such as work history and my current job, **** on my last renew I forgot to check a few boxes and left out an address for one of my references. Called them up expecting them to say come finish filling it out, nope they said it was approved and awaiting my pick up. They have never contacted any of the references I put down, I mean come on who the hell is going to put down someone they know will give them a bad reference? There have been some cases that people just put dead people down and they still get their permit. There is nothing stopping you from even adding yourself as a reference.
Unless you have the time and the money to fight the poilce department in court, the whole 14 days thing is more of a guide line to them(I said to them, even through it's a LAW.) They know the average Joe will not be able to do much about it should they take longer.