Racial Bias and the Death Penalty - Tharpe v. Sellers

Should a court pierce a jury's discussion to detemine if a verdict was improper on the basis of race? If so, is there any limiting principle, or should all grounds be valid? Does this ultimately do more harm then good (Habeas Corpus, 6th amendment Right to a Jury, 14th Amendment Equal Protection, The Antiterrorism and Effective Death Penalty Act)