It's a phrase to highlight someone missing the point, purposefully or otherwise. It doesn't matter how good the play was, Mary Todd Lincoln watching her husband and then President of the United States Abraham Lincoln get shot in the head right beside her overshadows everything. It could have been the best acting ever but that's not what she was focusing on or what she'll remember.
In reference to the Aurora shootings
Person 1: "Oh my God, that's awful! Was the movie any good, at least?"
Person 2: "Besides that, Mrs. Lincoln, how was the play?"
In reference to a controversial person
Person 1: "Yeah, Mike's an alcoholic, a tax cheat, beats his kids, and is a pathological liar â but other than that, he's pretty cool."
Person 2: "Besides that, Mrs. Lincoln, how was the play?"