During the long-shot of the Sycorax ship hovering above Rose's estate, the people standing on top of the buildings can be seen to be crude computer-generated images. Only five images are used and are repeated, and in several places overlap with each other, revealing their "flatness".
In the bedroom used by the Doctor, around the door damaged by the alien Christmas tree there are clear guide lines to help the carpenter cut out the tree shape.
When they are explaining how the space probe carried blood samples, the camera pans down to show a computer screen, but a media player is shown. Later, the media player is shown full screen. The computer interface must have just been recorded onto a movie file and played, but they forgot to make it full screen before filming.
The UNIT soldiers carry the same weapons as the guards on Satellite 5 in the 2001st century. The weapons are present-day G36 rifles, manufactured by Heckler and Koch so it is strange that the security personnel of Satellite Five would be carrying firearms manufactured over 200,000 years ago.
When the Doctor is proving his identity to Harriet Jones by telling her about when they were trapped together at Downing Street, his words don't match the movements of his jaw when we see him from behind.
The "blood control" the Sycorax use to control the population has everyone with A+ blood walk to the rooftops or tallest building near them. How, then, are people in airplanes or those who live in generally flat areas of the world affected?
When explaining information about Guinevere One there's a misspelling of the probe (Guinivere) twice.