While Judith is preparing to leave Jake with his father for the first time, the blind on the right side door from the deck keeps changing, from up to down, several times as Judith talks with Alan.
The bottle of Corona Charlie drinks on his porch changes its orientation (label visible/hidden) between shots.
When Charlie is in the grocery store with Jake and puts a carton of milk back on the shelf, it wobbles when he sets it down, indicating that it's an empty prop.
At approximately 13 minutes in, when Charlie says "I think he's considering it now, Mom", Blythe Danner's (as Evelyn Harper in the original pilot) red-and-white dress is visible in the left foreground.
Judith is staying with her sister in Las Vegas for the weekend, so there's no reason for Alan to stay at Charlie's house with Jake. He could just stay at his own house until Judith returns.