Mary Todd was definitely unstable, but 3 of her four sons died (at ages 3, 11 and 17 if I recall correctly) and her husband was assassinated while she was sitting next to him. Top that off with her only remaining son's attempt to have her declared insane, and you've got plenty of reasons for her to "have issues."
When Lincoln asked Grant to come see a play, Mrs. Grant told US that she wasn't going, on any terms, if it meant provoking another screaming match from Mary Lincoln. Grant begged off the invite, and Lincoln invited a military aide named Rathbone and his fiancee to see Our American Cousin.
If Grant and some of his staff had been tailing after the President, would Booth have gotten as close?