In the opening scene The Doctor has a plaster across the cheek of his face, but the next time he is seen the plaster isn't there, but he has a scar, which is obviously what the plaster was covering.
The Doctor tells Victoria that underground trains are a little after her time; however, Victoria is from 1866, and the first underground railway between Bishop's Road (now Paddington) and Farringdon Street was opened three years earlier, on 10 January 1863.
When Jamie places his hand down on the TARDIS console he quickly moves it off as if he burnt it.