The band bus is first shown with temporary paper license plates (white with red lettering), followed immediately by a close-up of the standard issue California black/gold plates to highlight the "Careful Nervous Mother Driving" sign on the rear. When its shown again from the front, they are back to temporary plates.
TV historian, Scott Awley pointed out a mistake in the scene when the kids are frozen on stage, and Shirley is trying to snap them out of it. She says, "Just imagine you're in the back of our garage, all five of us just having fun..." There are six members of the family, not five.
As the Partridge Family bus travels along Hollywood Boulevard, Danny points out Grauman's Chinese Theatre, and he and the other kids rush to the driver's-side windows to look. Outside the windows behind Danny, Chris, Tracy and Keith, the street scene is moving backwards, making the bus appear to be backing up instead of moving forward.
After they arrive in California, the audience sees the Partridge Family in a bus driving west on Hollywood Blvd. past Grauman's Chinese Theatre. But in the very next shot they are on Hollywood Boulevard, still heading west, but passing Vine Street (and the Capitol Records building), which is a mile to the EAST of the Chinese Theatre.