In the scene when Christian Slater's character is running down the hill after the Trolley in San Fransisco, you see many cars that are appropriate for the period lining the streets. If you look closely, however, you'll see Red-Zones. There weren't Red Zones in San Fransisco during this time.
Along with the warden's barracks, exterior shots of the island also show the rubble on the south end of the island when the apartments where many of guards' families should be seen, given the time period.
Although the movie took place in the late 1930s, all exterior shots of Alcatraz show the burned out shell of the warden's house. The warden's house on Alcatraz didn't burn down until 1970, seven years after it was closed as a prison, during the Indian Occupation of the island.