When Sam follows Frankie to the AA meeting, it's the middle of the day after Frankie took Josh home, but when they first speak outside the meeting's location, it's well after dark.
Very early in the movie Sam enters Jerry's room and the window he sits by indicates that it's night time, but as they leave the building it is morning.
Josh opens the door to their apartment with the key in the deadbolt, but doesn't turn the key for the deadbolt until after he opens the door a few inches. The sound of the deadbolt turning is audible after the door is open.
When Sam and Frankie are doing the laundry, Frankie's necklace is inside her shirt, the camera switches to Sam and when it's back to Frankie her necklace is outside her shirt.
When Sam and his mom are sitting on the couch after Lillian's operation, in the camera shot from the left she rubs her head with her fingers. Then the camera shot turns to the right, and she isn't rubbing her head.
When the sodium is thrown into the pool it sinks to the bottom before exploding. In reality sodium floats on water and the explosion is caused by sparks igniting the hydrogen that is formed.
About 1.5 minutes into movie Chris Pine says "There's a market for everything Phil Weyerhaeuser Paper...." Pine pronounces the company "wire-heiser", but the correct pronunciation is "ware-houser."