The Sound of Drums (2) - S3-E12
Continuity mistake: When the Master stands up on the Valiant to announce that he is the Toclafane's "Master", President Winters is visible in the background, only the Toclafane aren't there. In the next shot, they return, buzzing around Winters' head.
Suggested correction: This seems to be caused by angles - the Toclafane are floating fairly high up, around the level of Winters' shoulders and above, but the Master is lower down. Hence, why they're not visible in the shot.
The Sound of Drums (2) - S3-E12
Continuity mistake: When gassing the cabinet members, the Master puts on a gas mask. The Valiant logo is above the tube, and upside down. In the next shot, it is below the tube, and the right way up. (00:04:50)
The Sound of Drums (2) - S3-E12
Continuity mistake: In the conference room, Saxon (The Master) puts on a gas mask that has an emblem mounted above the hose. After replying to the question, he moves the mask, and the emblem is on the bottom of the mask.
The Sound of Drums (2) - S3-E12
Continuity mistake: When Martha starts to phone her family, after the Doctor warns her not to tell them anything, as she snaps in response, "I'll do what I like!", in the first shot she's holding her phone away from her body, but in the second shot it's jumped to her ear. (00:14:25)
The Sound of Drums (2) - S3-E12
Continuity mistake: When Jack tells Martha they have to ditch her car after escaping from the Master's thugs, the position of her hands on the steering wheel changes between shots. (00:17:05)
The Sound of Drums (2) - S3-E12
Continuity mistake: After the Master calls Winters "the last President of America", in a shot from behind him and Lucy, he has his hands by his sides. In the next shot, facing them, the Master has his hands clasped behind him. (00:31:35)
The Sound of Drums (2) - S3-E12
Continuity mistake: When the Doctor stops and raises his hand while he, Martha and Jack are running through the Valiant because he senses the TARDIS, his fingers keep changing position between shots. (00:34:40)
The Sound of Drums (2) - S3-E12
Continuity mistake: When the Doctor fixes Jack's vortex manipulator so they can escape the silo, Martha and Jack are holding the lab door mostly closed against a horde of Futurekind. In the shot where the trio time-travels away, the Futurekind, some of whom had stuck their hands through the gap in the door, are missing. (00:00:40)
The Sound of Drums (2) - S3-E12
Continuity mistake: At the beginning of the Cabinet meeting, when the Master says, "Thank you. Thank you, one and all," in a wide shot, he turns his head to his right. In a close-up immediately afterwards, his head is facing straight ahead. (00:04:00)
The Sound of Drums (2) - S3-E12
Continuity mistake: During the Cabinet meeting, when the Master stands up as he says, "That wasn't funny," in a shot from behind he places both hands on the table as he rises. In the next shot, facing him, his right hand is suddenly by his chin. (00:04:10)
The Sound of Drums (2) - S3-E12
Continuity mistake: When the Doctor talks about how the Master was always sort of hypnotic, in a wide shot, Martha is sitting on the end of her couch, with her hands loosely folded, with her left hand on top. In the shot of her where she says she was going to vote for Harold Saxon, her right hand is on top. In the next wide shot, her hands have reverted to their original position. (00:12:05)
The Sound of Drums (2) - S3-E12
Continuity mistake: On the Valiant's bridge, when the Doctor is telling Martha and Jack about his plan to slip one of the perception filter keys around the Master's neck while holding his key, the position of the key changes in his hand, from being held by the wide end to being held by the narrow end. (00:37:15)