When the camera cuts away after Tabitha spills her milk, the configuration of the spill is in a completely different pattern in the next shot.
Julius Caesar hands gold coins to the taxi driver, saying they are Roman sestertii. Sestertii were made of brass, aurei were gold.
Darrin ( Dick Sargent dressed as Caesar) opens a fake kitchen door into the hallway then slams the door, vibrating the fake door frame.
For years, Darrin (Dick York) occupied the den facing the doorway. The doorway had a clean shot into the kitchen, from one doorway through to the other. The fake kitchen door (that opens into the hallway) does not align correctly.
Julius Caesar refers to himself as "your Emperor ". He also refers to himself as "imperator" which is more correct. He would not refer to himself as that though. It was Augustus who made that title the sole preserve of Roman emperors in the sense we know it. Also he takes great umbrage in reading he was made "dictator". In Republican Rome the title didn't have the despotic connotation it has in modern times.
When Samantha shows Caesar the history book, showing him important dates in his history, he reads off dates with "B.C." in them, and doesn't ask what "B.C." means. Caesar died before the start of the Christian era, and would have no idea what "B.C." means. The dates would be totally meaningless to him because that was not the system of counting years used in his time.