This scene with Jimmy and Harry is so powerful. There's so much emotion and understanding without saying any of it out loud. Jimmy knows Harry is eaten up with guilt, and he gives him a perfect blend of sternness and kindness, without ever embarrassing Harry or specifically naming the thing they both know Harry feels guilty for. Jimmy really shines as a supporting character here. He is a good man, through and through.
This is a very touching scene. However, there are a few quibbles about it. To begin with, in the opening of this scene, which isn't shown here, Jimmy and Jo make plans to go spend the evening together, and Jo runs off to change. Yet, Jimmy seems to forget that when he makes plans to go out with Harry for a drink. And then, after his brief reunital with Jo, Harry apparently forgets about that and leaves (unless he met Jimmy outside after that). Finally, something else that didn't make this particular video. What happens next is, Jo runs onstage to perform again. And I thought she was done for the night, which is why she made plans with Jimmy. Just had to mention those things.
Jimmy didn't forget it. He knew Jo was about to come out and she'd run into Harry, and they'd reunite, so he made an excuse to get out of the way. As for her running back onstage, maybe it was an encore song after the show finished.
You're both probably right about Jimmy wanting Jo to know Harry was here, but I doubt it was an encore. If that was the case, Jo and Jimmy wouldn't have planned to go out until after the fact.