THE battle over Clarence Thomas's nomination to the Supreme Court - which begins its 1991-92 term today, the traditional first Monday in October - has focused attention not only on Judge Thomas's own qualifications, but also on the confirmation process itself, and its effect on the quality of judicial nominees. Whether or not Thomas is confirmed in the Senate vote scheduled for tomorrow, many questions will linger.There is widespread dissatisfaction in legal and political circles about the appointment process as it worked in this instance. The concerns, though voiced principally by people who oppose Thomas, are also held by thoughtful observers who generally share Thomas's conservative views. Among even the latter group are many who regard Thomas as an undistinguished nominee, a man whose opinions will not advance the clarity and intellectual coherence of Supreme Court jurisprudence. The Supreme Court nomination and confirmation process is more evidently political than ever before. In part, this may be the result of what is coming to look like an almost permanent division of the federal government between a Republican White House and a Democratic Congress. More than 20 years have passed since a Democratic president, Lyndon Johnson, appointed a member of the high court. Senate Democrats today may believe that in the foreseeable future, their only means to bring balance to the court is through the advice-and-consent mechanism. One may decry this politicization - whether one regards the problem as the political litmus tests used by Republican presidents in making judicial appointments or the political criteria used by Democratic senators in evaluating nominees - but the dynamics that brought about this state may not change soon. The biggest question is: In the present climate can men and women of genuinely high intellect, notable scholarship, and laudable achievement be appointed to the court, or will political factors crowd out such qualifications? This issue must be urgently looked at if we are to avoid future confirmation hearings that, on both sides, are anything but serious attempts to take the measure of a nominee's legal mind and skills.