When Charlie is sitting at his piano, writing down some lyrics for a jingle he was creating, he clearly just scribbles a few lines on his pad of paper and never actually writes any words down.
It is highly unlikely that Charlie and Alan would wear their Disneyland hats all the way from Anaheim to Malibu as shown, walking in the front door, wearing the hats. No doubt, they would have just taken them off in the car and just carried them into the house.