At the cemetery, Brenda gives Nate her phone number, but she had already spoken to him on his cell phone which would have have identified her number.
During a flashback Nate Fisher Sr is shown embalming a body while smoking; the embalming fluid that would've been used at the time was highly flammable and even explosive when mixed with acids so it was used under strict safety procedures that didn't include a lit cigarette.
It wouldn't have been necessary for Nate to identify his father's body in the morgue since he would have had a driver's license in his wallet and registration in the vehicle to identify the owner.
The hearse in the opening credits has a Washington state license plate.