Visible crew/equipment: When Jack goes out to the main room half clothed to answer the door, the tip of the boom drops several times on the way out, and when he 'stumbles' backward. Then, when he and Vicki are seated while having dinner with her father, you can hear cabinet doors opening and closing from somewhere on set, and a bit of equipment moving around behind Vicki.
A Case of Sour Grapes - S1-E14
Other mistake: There is a sour bottle of wine that Jack and EZ taste in the kitchen - Jack throws the bottle in the sink and breaks it before Vicky and Mr. Bradford enter the kitchen and have a chance to taste it. There would be a strong sour smell all over the kitchen, but no-one in the room noticed any bad smell after the bottle of wine breaking.
