When Cassandra vanishes into the time portal in 2155, her discarded cloak vanishes with her. When she arrives in 1978, the cloak does not arrive with her.
When Cassandra mounts the horse to flee the mine, she is wearing brown high-heel boots. When Wonder Woman lassos her from the horse, she is wearing black sneakers.
When Clement tries to get away in the black AMC Matador, he is seen trying to start the car by fooling around with several different things on that cars dashboard, one of which is the cars radio. The radio he's shown fooling around with has a horizontal dial. The AMC Matador of that era had a radio with a vertical dial on it.
The time travelers go back to 1978 Washington D.C. yet the Griffith Observatory is in California. The scene with the sniper clearly shows the landscape of Downtown Los Angeles.