For my own picks I would throw in
-James V Forrestal: He was a decent fellow before 1945 but following a short little trip to shore during the Battle of Iwo Jima something snapped in the man. Hardliner Anti-Communism with a belief that the world was doomed to end in nuclear hell fire in his lifetime, his politics zig-zag issue to issue from Henry Wallace to Strom Thurmond, while he would have done some good there's alot of unpleasantness mixed in.. The growing crazy, behind the veneer of determination, hard work ethic, and moral strength means he could probably make it to the office, and then we have a suicidal nutcase with the nuclear football. And in 1948 there were some major Democrats who thought dumping Truman for him was a good move.
- Charles W Bryan: The younger brother of the previously mentioned William J, lacking most of the intellect, and the morals. The Democrats in 1924 would have put him one heartbeat away from the presidency, and that heartbeat (And the whole ticket) was one being backed by a bunch of bed sheet wearers. Sided with them in that wonderfully close vote that year at the convention to condemn the Klan or not. Fearing it would damage his chances he voted for the hooded order. I'd include John W Davis but I'm pretty sure most people already know about him.
-Robert Byrd, Richard B Russell, Jesse Helms, Barry Goldwater, Strom Thurmond: Obvious reasons, even if you really belived that they changed later in life, opposition to the Civil Rights and Voting Rights acts in the 1960's shows a lack of moral character prohibitive to the top office. Other awful domestic and foreign policies certainly follow.
-James F. Byrnes is like the group I just listed, except he almost got the job, with FDR liking the Southern Segregationist for the post of VP in 1944, and only getting blocked by Party bosses who thought they couldn't bring in the votes for him.