The rubber band is slack when it is first attached to the door frame, but taut after it fires the rock.
After Sylvester uses the inner tube to shoot the rock thru the front door and into the wolf, Little Red Riding Hood and Tweety run out of the house thru the same door, but the inner tube that was stretched across the doorway is now gone.
The sign that reads "To Grannys" should be "To Granny's"
At 4:13, Sylvester and Big Bad Wolf pass through each other.