Why would he have corrected himself? That would've worked against the impact of the moment even worse. Using her first name wasn't a mistake, it was a meaningful gesture, an acknowledgment of what she's come to mean to him. And that spoke volumes on its own without her needing to state the obvious. Nicole Beharie could've sold her reaction with her face alone, because she's awesome. She didn't need the words as a crutch.
Perhaps the dialogue was a bit unnecessary, but I think the spoken sentiment worked better because of how she nearly choked up as she delivered the line. The show is still fairly new so maybe the producers were hesitant to allow a remarkable moment to slip by without a, ya know, remark. Spoon-feeding the newborn viewers who may not have seen every episode and understood the significance of him calling her "Abby."
Speaking the line or not speaking the line, I will completely agree with you on the actress' awesomeness.