Have the witches make a mistake about Banquo's sons becoming kings?Because it did not happen that way. Instead of Banquo's son, Malcolm, king Duncan`s son, is crowned king at the end of the play.
No, they have not made a mistake. In Act 1, they tell Macbeth and Banquo that Macbeth will be king and that Banquo "shalt get kings, though thou be none". Later, Macbeth realizes that he has to kill both Banquo and Fleance, Banquo’s son, to prevent this prophecy from coming true. Macbeth plans to have both Banquo and Fleance murdered, but when the two men are ambushed, Banquo fights off the attackers and tells Fleance to get away. Fleance escapes. When Macbeth learns of his escape, he is quite upset:
"Then comes my fit again: I had else been perfect, / Whole as the marble, founded as the rock, / As broad and general as the casing air: / But now I am cabin'd, cribb'd, confined, bound in / To saucy doubts and fears.”
At the end of the play, the witches meet up with Macbeth again and show him the vision of a long line of kings descended from Banquo, so although Fleance is not the king right now, the witches show that his descendants, indeed, will one day rule Scotland.
No, the witches did not make a mistake in their prediction that Banquo will "[be]get kings but not be one." The play was written and performed for King James 1, who was a descendant of the actual Banquo. James was a Stewart from Scotland; the Stewarts took the Scottish throne in the 11th century, when this play took place. Shakespeare's audience would have been well aware of this fact. The witches never say when Banquo's descendants will ascend the throne, just that they will.
In Act 4, the apparitions show a long line of Banquo's descendants as kings, one showing an image of a king holding "twofold balls and treble scepters," indicating the union of England, Scotland, and Ireland in 1603 when King James VI of Scotland became King James 1 of England. The last one holds a mirror, expressing Shakespeare's wish that the Stewart continue to rule successfully in the future.