In the Season 5 opening, as Barbara Billingsley comes out the door to offer refreshments to Ward, Wally and Beaver, she has both hands holding the tray, but the door opens and closes without her having to touch it. In the crack of the door on the left side, there is a glimpse of someone in a white or light colored shirt behind the door.
In the title sequence shown before each episode in Season 6, each family member comes out the front door on their way to an outing in the car. About halfway down the walk, Barbara Billingsley looks directly at the camera (it's called 'breaking the fourth wall', usually a no-no), seeming either to say, "How's that? Am I doing OK?" or, "I'm not going to run into the car, am I?"