Plot hole: Jo is surprisingly skeptical about the TARDIS being able to move, considering she saw it dematerialise in the last episode.
Factual error: The calendar which shows the date to be Monday, 2nd March, 2472, is two days out. 2nd March 2472 will be a Wednesday. And who made the calendar if the colonists left Earth over a year earlier?
Answer: TARDISes are generally available for properly authorised use on Gallifrey; they're not usually assigned to a particular Timelord on a long-term basis. The Doctor stole his when he left his homeworld.
Tailkinker ★