Rob tells Buddy and Sally the night after the argument that he spent the night in the garage because he left his keys in the house and didn't want to go back in to get them and face Laura. However, we see that he left with all of the things he had when he came home--he did not leave his keys in the house.
He said that he ran out without his car keys, yet he got into work the next morning. Even if he took the commuter train he'd still have to get to the station, and he had no phone to call a cab.
At the end Rob is having spaghetti for dinner. However he picks up chopsticks to use to eat the spaghetti. Laura was the one with Chinese food, not Rob. There is no reason for Rob to be using chopsticks.