(at around 1 min) During the scene where Winston goes back with the pink letter to Don's home, after he turns down the volume he sits down we can see the lampshade on the side table changing position to the next scene when the pink letter is on the table in front of Don's couch. This can be seen on the profile shots of Don and the lampshade on the background relative to unchanged camera angles.
Around the 1hr mark of the film, after Don gets off the plane and is driving over the bridge, his sunglasses appear on, then the camera angle changes and the sunglasses are off, then on again at the next camera angle change, with no indication that he had taken them off
When Don is about to leave for his road trip, the flowers on his fireplace are shown in a decaying state, with petals laying around the vase. When he returns from his road trip, the same clip is used to show the flowers again in the exact same stage of decay.
As can be evidenced by the symbols on the airport signs (the letters A, B, and C, individually, are in the center of rounded triangles, designating sections of the airport) Newark Airport (NJ) was used for each of the airport scenes, although Murray's character was supposedly going to many different places in the US.