Whether it was accurate or not, I thought the sight of them together in bed at the end was an inspired moment-- just because of how perfectly normal and modern it all looked.
The only thing I thought didn't work at the end was the odd misdirect of the final theater scene. I'm not sure what the point was in making us think we were about to see Lincoln get shot, only to reveal that it already happened somewhere else.
Actually I sort of liked that. Because almost everyone who watched the film knew that Lincoln got shot in Ford's Theater. It's a scene that many are familiar with so I liked the idea of seeing the assassination from another angle.
It was confusing at first. I hadn't heard anything about his son being with him at the theater but once I saw what Spielberg did I liked it. It showed the emotional reactions from his son and the people, it showed how much Lincoln was loved and admired, of how painful his passing would be for the nation.
Perhaps Spielberg could've done a little better job showing what happened after the shooting, instead of going all gauzy with his camera. Also I wish they had shown that other people were also attacked that night. But then again, that might have took away from the misdirection/alternative angle he was going for.