Barbara Pepper, the only other woman in the Friends of the Friendless besides Lucy, appeared in many installments of the series. When the Friends of the Friendless first arrive in the park, Barbara is wearing a hat. As she passes under a tree, her hat gets caught and it falls off. She doesn't stop to pick it up, and even at the end of the scene we don't get a chance to see her pick it up as she leaves the park. Since the series was shot like a play in front of a live audience, retakes were not usually the norm for the cast.
Mrs Trumbull ends up babysitting Little Ricky during Lucy's party, but no one had made arrangements for her to do that. The other three leads knew that Lucy would have to leave the apartment that night, and everyone else would be at the surprise party, so a babysitter would be needed. But it's not until Mrs Trumbull calls Ricky to scold him (for apparently forgetting Lucy's birthday) that the topic of watching Little Ricky comes up--and even then, it's Mrs Trumbull who offers it, not Ricky asking her.