Anne Reed at Deliberations explains the U.S. Supreme Court's unanimous decision on "peremptory challenges" to potential jurors yesterday in Rivera v. Illinois, No. 07-9995 (U.S. Mar. 31, 2009). Bottom line: A judge's good faith error in rejecting a peremptory doesn't entitle you to a new trial.
That presumably applies not only in criminal cases (like Rivera) but also in civil ones.