Final answer:
Grounds for judicial disqualification that cannot be waived include the disqualification of individuals who engaged in insurrection against the U.S. under the 14th Amendment, and the impartiality of jury selection as mandated by the Sixth Amendment for both criminal and non-partisan election contexts.
Step-by-step explanation:
Parties and lawyers may agree to waive any grounds for judicial disqualification, but there are exceptions where waiver is not permitted. For example, under Section 3 of the 14th Amendment, persons who have taken an oath to support the Constitution and have subsequently engaged in insurrection or rebellion against the United States are disqualified from serving as president. This specific ground for disqualification cannot be waived unless by a two-thirds vote in both houses of Congress. Additionally, impartiality in jury selection is another example where parties cannot waive disqualification, as potential jurors cannot be systematically excluded based on race or sex to preserve the Sixth Amendment's requirement of an impartial jury.
In the context of impeachment, the Constitution makes it clear that a party convicted by impeachment not only faces removal from office but is also disqualified from holding any office of honor, trust, or profit under the United States. This type of disqualification is also non-waivable. Furthermore, when considering the role of judges in trials, the Sixth Amendment ensures the right to an impartial jury, and both parties have the right to reject potential jurors. However, this does not allow the exclusion of jurors on the basis of race or sex.