When Diego and Luther are talking just before receiving the invitation, when camera is looking at Diego, there is sun behind him, casting sun spots at Luther. When looking at Luther, he is in shadow.
When Klaus, Vanya and Allison are conversion in the beauty parlor, Allison puts her feet up on a stool. In a long shot her feet are down and she is leaning forwards, and in subsequent shots her feet are up on the stool again.
The Grosser Mercedes shown in the 1963 scene has the side running lamps and retro-reflective markers, which wasn't mandated in the United States until 1968.
Harlan is playing the Milton Bradley game Operation, but it wasn't released until 1965- two years after the events in this timeline.
While Sissy and Vanya are laying in bed together "Love in the City" begins to play, it's supposed to be 1963 but "Love in the City" by John Stokes isn't released until 1974, 11 years after this is taking place.