In the first scene, the subtitle gives the date as May 1, 1939, which is said to be seven years later. However, Part V (1932-1933) (1979) ended in the summer of 1933.
Simon says that Alex's full name is Alexander Murray Palmer Haley and that the name Murray links him to his great-grandfather Tom the blacksmith. This was indeed the real Alex Haley's full name. The Murray is for his maternal grandmother Cynthia's family and was in turn taken from the family to whom they belonged as slaves until the end of the Civil War. However, in Roots (1977), the owners were named Harvey so this should have been one of his names.
In English, "yerba buena" translates to "good herb". It's a name given to several aromatic plants. Does not mean "peppermint"
When Simon Haley is talking to his son about his career prospects after he has dropped out of college, at one point he addresses Alex as Simon.