When Nelson Van Alden opens the divorce papers from Rose, it says "U.S. District Court". Federal courts do not issue divorces, which are the responsibility of the states.
Van Alden opens an envelope with a Summons for a divorce petition. Under no circumstances would this be correct service of the Summons. He lives out of State and the envelope contains his wife's return address. To be valid he must be PERSONALLY served, not simply receive a first-class envelope from the opposing party (i.e., his wife).
Randolph has Eli picked up on a murder charge, in the Hans Schroder killing. Murder is a state crime, not federal. Even when JFK was murdered in Dallas, the assassin would have been tried in a Texas court.
In the church where Margaret is praying for Emily's recovery, to the left of the sanctuary there hangs an image of the "Divine Mercy" Jesus, common in Catholic churches nowadays. However, that particular devotion began in the late 1930s and only reached the United States in 1941, 20 years after the events depicted.