Odds of Getting In
Residency and top fellowship programs are very competitive, as are the top med schools, of course. However, once you're in and if you do well, you'll have a built in network of referrals to get your career going and will probably have a job waiting for you, as many hospitals are always on the lookout for good endocrinologists.
The field is wide open and this specialty is very much in demand, so you shouldn't have to worry about finding work if you have the right skills and credentials.