Odds of Getting In
If you can stick it out through medical school and residency without dropping out (or being gently told to leave), you shouldn't have a problem finding a job in the field. Generally speaking, physicians and surgeons have a job growth outlook of eighteen percent (source). Health care reform and a generally aging population are partly what's driving that growth. Aging people definitely need neurological care. An estimated 5.1 million Americans currently suffer from Alzheimer's, and this figure is expected to rise as the population continues to age (source).
If you want to up your odds, the highest amounts of job vacancies for neurologists in the U.S. are in Utah, Idaho, Nevada, and D.C. (source).