Continuity mistake: When the Doctor enters the desert room in addition to his coat, he is wearing a brown waistcoat with a white shirt underneath. When the shot cuts away and the back to the Doctor, we see him take off his coat but he is no longer wearing the waistcoat. Later when he collects his coat after the acid bath scene and he starts to look through the wardrobe for a disguise he is mysteriously wearing the waistcoat again.
Revealing mistake: In the last part, the giant robot steps on a soldier. There are several things wrong with this scene. 1) You can see the matte halo around the robot's foot. 2) The robot does not leave a footprint. And 3), after the soldier gets squashed, his arm is visible waving over the robot's foot.
Visible crew/equipment: (Part 3) After Omega has revealed himself to the Third Doctor, Jo, and Dr. Tyler, when he begins to speak privately to the Doctor the camera casts a shadow on Omega's body. Then after Omega turns around the boom mic dips into view at the top of the screen. And when Omega starts walking forward, the shadow of equipment (presumably the boom and mic) can be seen moving on the far wall, near the lower left of the screen. (00:03:10)Super Grover
Continuity mistake: In the cliffhanger to episode 1 of this story, as the Daleks approached the TARDIS, the TARDIS door was open. At the beginning of episode 2, seconds after the cliffhanger moment in 1, the door is suddenly closed. (00:01:00 - 00:02:00)Captain Defenestrator