Plot hole: Yartek tried to disguise himself as Arbitan by wearing Arbitan's robes and pulling the hood over his giant rubber head. Strangely enough, no-one seems to notice that "Arbitan" is now suddenly speaking with a completely different voice, and now has a two-foot-tall-head.
Plot hole: The miniaturized TARDIS crew never interact with the other characters in this story, because, as the Doctor points out, the 'giants' will be unable to hear them, as their voices will be on a different wavelength. So why does the Doctor later suggest using the telephone to try to call for help?
Plot hole: How did UNIT soldiers manage to get the TARDIS through an ordinary door into the Doctor's dorm in the research centre? The Doctor's labs in the various UNIT HQs had either double doors or a removable partition wall. The research centre is supposed to be an ordinary country house with single doors and solid walls. The TARDIS is larger than the average wardrobe and, unlike most modern wardrobes, doesn't come apart so it can be got through doorways. The TARDIS is known to be a "Type 40 capsule"...but there's never been any mention of the TARDIS being an IKEA-style "flat pack self-assembly" time machine...
Plot hole: When the Doctor goes into the CET projection of Eden, to fight the Mandrells, he disappears into the bushes on the left-hand side of the screen. Cue much shaking of foliage, and Tom Baker's cries of 'ooh', 'aargh' and 'ouch'. The Doctor then reappears with his clothes all tattered and torn, due to his 'fight' with the Mandrells...but the the fact that there is not a mark (not even a scratch) on Tom Baker is something of a giveaway that all Tom Baker did was disappear behind some bushes and do a quick change into a tattered version of his costume.
Plot hole: Azmael doesn't recognise the regenerated Doctor (In the shape of Colin Baker) whereas on most other occasions other Time Lords do recognize each other through telepathy. This is odd behaviour by Azmael, considering that Azmael and the Doctor HAVE actually met before, and possibly more than once. (Azmael last met the Doctor in the Doctor's fourth incarnation, and was the best teacher the Doctor ever had. On that occasion, Azmael got drunk.).
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? (00:15:10 - 00:22:10)
Plot hole: When the airlock door is opening at the end of the final episode, the Cyberman is the only one who appears to be affected by the air rushing out. Although 'rushing out' is probably overstating the speed of the 'explosive decompression'. It's not so much an explosion as a gentle breeze...
Plot hole: In episode 4, watch what Romana does to Professor Kerensky's time machine in order to make it work. It is surprising that the time machine works at all, considering she is supposed to be in Paris at the time. Romana wires up the time machine to a British (i.e. 3-pin 240 volts) electric plug instead of a "continental" 3-pin 110 volt plug.