Plot hole: Just after the Doctor meets the Brigade Leader, he looks at the countdown and says in a very loud voice, "only 3 hours and 22 minutes". Several minutes later, when he leaves the office after stunning Benton, the countdown still reads 3 hours and 22 minutes. Did the countdown clock stop?
Continuity mistake: In episode 1, when the Doctor opens the garage doors with his 'door handle', note the two men in the background, the position of the car behind him and the white pillar. In the next shot, the men and pillar disappear and the car moves to a different spot. In the shot after that, the tanker truck is now parked in front of a pillar. You can see near the beginning of episode 3 that there are two entirely different buildings that the tanker had been filmed in front of.
Continuity mistake: There are a handful of similar continuity errors, but one that stands out in particular occurs at the end of Episode 1. The Doctor and Liz go into the lab and Taltalian steps out from behind the door wearing glasses and brandishing a gun. However, in the recap at the start of episode 2 he isn't wearing glasses and moves differently.
Audio problem: When the Doctor arrives at UNIT HQ in his stolen car, he speaks to a guard. We see close ups of the guard twice...but watch the brief clip of The Doctor (Jon Pertwee) between the two and you can just see that his lips aren't moving even remotely in synch with the words. (In fact, it is just a repeat of the previous shot of The Doctor, with new lines dubbed in).
Continuity mistake: At the beginning of the third episode, the countdown reads 49:18:32 in the close up, but when the Brigadier walks across the room it now is on 49:15:01. (In other words three minutes thirty one seconds have elapsed). Yet these two events are about ten seconds apart. Also, the timer should never read either of these times. The professor moved the countdown forward to exactly 49 hours (49:00:00).