In 17 years in business, I live by one rule of thumb when it comes to time sensitive documents and the USPS.... Never trust them, not even priority service. The chances of the package being lost, late, or damaged increases directly with the importance of the package.
I've lived at my current address right at 9 years now and I cannot count the number of times I have gotten my neighbors' mail. Heck, that's how I met most of them, hand delivering what was delivered mistakenly to me.