Evidence
Truthfulness
The truthfulness of a witness is always relevant to the case, so testimony about a reputation for untruthfulness or opinion of untruthful character can always be admitted. FRE 608(a).
The truthfulness of a witness can only be bolstered by a character witness if it has been attacked by the other side. FRE 608(a).
Attacking a specific instance of untruth is not attacking the person's truthfulness and therefore does not open the door to character evidence of truthfulness.
Except for a criminal conviction under Rule 609, extrinsic evidence is not admissible to prove specific instances of a witness’s conduct in order to attack or support the witness’s character for truthfulness. But the court may, on cross-examination, allow them to be inquired into if they are probative of the character for truthfulness or untruthfulness of:
Specific instances of crimes one is convicted for cannot be admitted under FRE 608, only FRE 609.
Saying that one is mistaken is not saying that one is lying or that he is a liar. It is just impeachment by contradiction and only possibly prohibited by FRE 403's test for unfair prejudice or wasting time.