I’d just like to pick up on a couple of points that you made.

She had expected Dan to pick up on her insult.

This is something you would expect a skilled negotiator to pick up on.

She’s always picking me up on my grammar.

This is something you would expect a friend to pick up on.

She had expected Dan to pick up on her lead and take the story further.

I’d just like to pick up on a couple of points that you made.