When Fred and Barney go to the club, they park right in front of the front door. When Betty and Wilma arrive, they park in front of the door, and Fred and Barney's car is gone.
When Hot Lips Hannigan moves his clam-shell mic to Fred Flintstone while introducing him, Hannigan's voice does not drop off.
Fred while practicing his magic acts including the disappearing egg trick, should have known the disappearing box had a secret back door and not been surprised when Wilma and Betty vanish.