Relevant passages from the version the Whitehouse is getting:
(1) UNLAWFUL ENEMY COMBATANT- (A) The term `unlawful enemy combatant' means--§ 948a(1). So the President has the power to declare people enemy combatants. It looks like § 950g gives the D.C. Circuit Court of Appeals jurisdiction to hear appeals, and the Supreme Court after that, so at least there's some judicial oversight. However,
(i) a person who has engaged in hostilities or who has purposefully and materially supported hostilities against the United States or its co-belligerents who is not a lawful enemy combatant (including a person who is part of the Taliban, al Qaeda, or associated forces); or
(ii) a person who, before, on, or after the date of the enactment of the Military Commissions Act of 2006, has been determined to be an unlawful enemy combatant by a Combatant Status Review Tribunal or another competent tribunal established under the authority of the President or the Secretary of Defense.
(b) Standard for Review- In a case reviewed by it under this section, the Court of Appeals may act only with respect to matters of law.§ 950g. Beyond that,
(c) Scope of Review- The jurisdiction of the Court of Appeals on an appeal under subsection (a) shall be limited to the consideration of--
(1) whether the final decision was consistent with the standards and procedures specified in this chapter; and
(2) to the extent applicable, the Constitution and the laws of the United States.
(a) Finality- The appellate review of records of trial provided by this chapter . . . are final and conclusive. Orders publishing the proceedings of military commissions under this chapter are binding upon all departments, courts, agencies, and officers of the United States, except as otherwise provided by the President.§ 950j. The bottom line? Avoid being wrongfully accused.
(b) Provisions of Chapter Sole Basis for Review of Military Commission Procedures and Actions- Except as otherwise provided in this chapter and notwithstanding any other provision of law (including . . . any . . . habeas corpus provision), no court, justice, or judge shall have jurisdiction to hear or consider any claim or cause of action whatsoever . . . relating to the prosecution, trial, or judgment of a military commission under this chapter, including challenges to the lawfulness of procedures of military commissions under this chapter.