The gun Ellen uses when with Patty is a different make and model from the one Tom gives her earlier.
When Ellen is in the car with the FBI in the final sequence, her hair switches from curly to straight (it is straight when she says "Because I know Patty").
At around 8.5 minutes in - The bearded uses a key to enter the hotel room wearing no gloves. As the camera flips to inside the room and you seem him coming into the room wearing a black glove on the hand he'd just used the key with.