The Vinvocci spaceship is said to be 105000 miles in orbit but space is only about 60 miles from the Earth's surface so the ship can hardly be in orbit at that distance.
There is no maximum distance at which one object can orbit another. The moon orbits the Earth at an average distance of 238855 miles.
When Verity is autographing her grandmother's published "Journal of Impossible Things," it's clear that the marker she's using isn't writing on the page.
The internal view ports of the Vinvocci salvage vessel are hexagonal, while the outer computer generated view shows them as being rectangular with rounded corners.
Donna's lottery ticket is rather a strange one in that the numbers are not printed in ascending order - 18 09 13 36 24, and the last one obscured by her fingers.
There are significant and obvious differences between the dental structure of The Master between his real (actor) self and skeleton (generated) self.
When Wilf is gazing out of the window of the spaceship at Earth, for the first time, the Doctor runs past and around the corner before coming back around after a moment to speak to him. However, it is obvious that David Tennant simply stops around the corner and pauses, before turning back. (Notice his feet are still visible, and the unnatural way he strides out.)
When the Doctor visits Rose at the end of the episode, she tells him the date is "2005, January 1st". Rose then runs into a building where on the glass by the doorway is a sticker stating "NO SMOKING. It is against the law to smoke on these premises." This type of sticker only appeared after the smoking ban in England came into force on 1st July 2007, two and a half years after it appears in Rose's building.
During the time lords' discussions one of them talks about "the TARDIS". Time Lords would talk about A TARDIS. The Doctor's vessel is not unique or in any way special to the Time Lords and they would not think of The Doctor's as a singular machine.