The Doctor has obviously forgotten his vow to Peri at the end of the Sixth Doctor episode "The Two Doctors", where he stated it would be a healthy vegetarian diet for the both of them from then on, since in his dinner with Margaret he orders steak and chips.
The Tardis is powered by the eye of harmony, a black hole, there would be no need for them to recharge or refuel.
When Margaret is being photographed, she notices it when the flash goes off so the picture of her has been already taken when she raised her hand to shield her face and demanded not to be photographed. However, her picture in the newspaper shows her with her hand raised. However, a second photo could have been taken a split second later and the newspaper's photo editor preferred that one for some reason.
(at 14:50 ) When Captain Jack leaps over the tea trolley in the hallway, the springboard he uses is clearly visible on the floor.
The 'earthquake' that takes place in this episode results in CGI-created cracks in the pavement that are very unconvincing. They do not appear to displace anything and - in a related continuity error - the cracks disappear in shots taken from ground level (the cracks are only visible in high-level 'looking down' shots).
Since "Margaret" had a teleporter, there was no need for her to climb out of the window and give the Doctor and his team a foot chase.