Veterans' Benefits Enhancement Act of 2008 - Revises or adds federal veterans' benefits provisions to, among other things: (1) reduce the waiting period for a veteran's affirmation of enrollment in a correspondence course; (2) eliminate the requirement that a veteran or beneficiary make a separate application for a program change at an educational institution; (3) eliminate a minimum wage-earning requirement in the case of self-employment on-job training; (4) authorize the Secretary of Veterans Affairs to stay adjudication of a veteran's claim when necessary to preserve the integrity of a Department of Veterans Affairs (VA)-administered program; (5) authorize memorial headstones or markers for deceased remarried surviving spouses of veterans; (6) make permanent the VA authority to fund contracted medical disability examinations; (7) expand Servicemembers' Group Life Insurance coverage to certain members of the Individual Ready Reserve; (8) allow VA to provide temporary residence assistance grants to active-duty military personnel suffering from a disability incurred in or aggravated by such service; (9) make permanent the consideration of noninstitutional extended care services as covered medical services; (10) make permanent the authority to provide hospital care, medical services, and nursing home care to certain veterans who participated in Department of Defense (DOD) chemical and biological testing; (11) provide third-party payment authority with respect to care furnished to spina bifida-affected children of Vietnam veterans; (12) authorize disclosure of VA medical information to a representative of a patient who lacks decision-making capacity; (13) require VA patients to disclose health-plan information and their Social Security number; (14) expand the authority of VA police officers; and (15) increase from $600,000 to $1 million the threshold before a VA major medical facility lease must receive congressional approval.