On season one of American Horror Story, it was established that the ghosts of those who died on the Murder House grounds could not ever leave those grounds except on Halloween. When Violet's ghost attempts to leave the grounds, she immediately appears back in the house the instant she would have moved off the property. However, on the day after Halloween (Episode 5), the security guard drives Hayden's ghost away from the house and speaks with her in the car en route to the police station. Her ghost vanishes (presumably back to the house) before they reach the station, but she clearly was in the car and off the Murder House grounds on the day after Halloween. Was this ever explained on the show or by the show's creators? Or was it a mistake?
No, she was in the car during Halloween, she vanished from the car when sunrises and end Halloween.
According to many mythology days don't start at 12 but after sunrise.
Even from the fandom episode synopsis:
As the sun begins to rise, the ghosts whose souls are trapped within the house return including Hayden, who vanishes from the back seat of Luke's car.