This is supposed to be the same apartment that Punky grew up in. When they go out to the car you see the buildings on each side are older taller buildings. But when you look at the footage from the original Punky Brewster (1984) season 3 episode ten (Fighting City Hall) the buildings on each side are significantly shorter.
When Izzy supposedly steals the blanket from Punky, it is obviously pulled from the side of the bed, and when Punky tries to steal it back, someone is holding it so it won't move.