'Pyramids of Mars' is often accused of having plot holes. In fact, I can think of three potential plot holes, but only one of them actually bothers me, and that only slightly. The first of these is that the Osirans entombed Sutekh with everything he needs to escape, but this is obliquely addressed in the script, the Doctor firstly explaining that the Osirans' moral code forbade them from executing Sutekh and later telling Sarah that they had "cerebrums like spiral staircases" and were known for their guile and cunning. The implication is that leaving Sutekh with a chance of regaining his freedom is part of their moral code, and this is further implied by the fact that the traps in the Pyramid of Mars are dangerous but passable; certainly, this is the assumption made by Justin Richards in 'The Sands of Time'. The second supposed plot hole is that having Scarman build the Osiran war missile in England is pointless, since he could have constructed it outside Sutekh's tomb, but again this isn't really a plot hole, given that it makes sense for Sutekh to exploit the fact that Scarman owns a large and secluded estate. The third plot hole is that the Doctor is rather fortunate that Sutekh decides to travel to England to start his revenge, thus allowing the Doctor to destroy him, and it is this slight flaw that bothers me, since he could easily have destroyed the world from Egypt. On the other hand, he may have wanted to collect his remaining Servitors before launching his reign of death. But even if this is construed as a plot hole (it is undoubtedly a plot contrivance to allow the Doctor to triumph), it doesn't matter; 'Pyramids of Mars' is a story that confidently papers over its limitations with a great deal of style and atmosphere.
'Pyramids of Mars' is unusual (although not unique) in that every supporting character except for the briefly glimpsed Egyptians at the beginning is killed off during the course of the story. This is significant, because it demonstrates on a small scale the horror represented by Sutekh, as one after another characters are casually slaughtered at his behest. This works particularly well because Holmes and Griefer create characters that are uniformly well characterised, regardless of importance to the plot, so that every death has an impact. The first example is Collins, the old and weary butler who has remained in the service of the mysteriously absent Professor Scarman partly because he doubts that he could find a new appointment at his age, but probably also out of a sense of loyalty. He appears only briefly, but is rather likeable and Michael Bilton gives him a plaintive air that makes his death at the hands of the Servitors all the more traumatic. Warlock is an even better example, forcing his way into Scarman's house out of concern for his friend and paying the ultimate price, and his death also feels tragic, partly because he has survived being shot by Namin, but also because it is ultimately Scarman who orders his death, whilst under the control of Sutekh. The best example of this principle is Lawrence Scarman. Lawrence is superbly portrayed by the ever-reliable Michael Sheard, and lasts for nearly three episodes, during which time we see his almost childlike fascination with the Doctor's alien knowledge (the scene in which he bounds enthusiastically around the TARDIS is charming), and also his gnawing anguish over his brother's ghastly fate. His interference with the Doctor's attempt to block Sutekh's control of Marcus and the Servitors literally endangers the entire universe, but it is painfully understandable and it is hard not to feel sympathetic as guilt is added to Lawrence's emotional burden. His death at the smoldering hands of his brother is heart-rending, and because of this the Doctor's subsequent dismissal of Lawrence's death works so well in reminding us of the true scale of the threat posed by Sutekh. The usually compassionate Doctor is so focused on stopping Sutekh that he can't waste time with individual deaths, and this more than anything else in the story is the true measure of Sutekh's power. Even Ibrahim Namin's death is powerful, as this faithful servant of Sutekh is casual dispatched by Sutekh's puppet as a reward for his service, and the same is true of Marcus Scarman, as he briefly regains his freedom from Sutekh in Episode Four, only to disintegrate into a charred husk.
Sutekh is vital to the success of 'Pyramids of Mars'. I praised 'Genesis of the Daleks' for its portrayal of Davros as one of Doctor Who's greatest villains by presenting him as a villain whose sense of morality is totally opposed to the Doctor's. With Sutekh, that principle is taken far, far further. He is perhaps the ultimate villain, a being of immeasurable power entirely devoted not to death or the subjugation of others, but to the total extermination of all life, everywhere, forever. His instruction to Scarman that after the missile is completed all life within the deflection barrier right down to birds, fish and reptiles must be destroyed because all life is his enemy is disturbing; no other villain in Doctor Who is so nihilistic. And whereas Davros is ultimately a man in a wheelchair whom the Doctor can physically overpower and in other respects face on an equal footing, Sutekh is effectively a God. The scene in which the Doctor confronts Sutekh in Episode Four is extremely powerful, Sutekh casually torturing him for every minor insult and explaining that all life must end under his reign. Gabriel Woolf's chilling tones drip with evil, helping to emphasize Sutekh's total malevolence, and mention must also be made of the rather sinister, but only briefly seen, jackal-like face beneath the impassive blue mask.
If the human cost of Sutekh's evil is well conveyed by the deaths of the supporting characters, then the large scale consequences of his escape are served by the scene in Episode Three in which the Doctor takes Sarah to a 1988 in which Sutekh was not stopped. The brief sight of the blasted, lifeless Earth is highly effective, further demonstrating Sutekh's power without blowing the budget, and also implying interesting things about time travel, given that it suggests that the Doctor's defeat of Sutekh has always happened and is already a part of history even before he succeeds.
The characterisation of the Doctor here also stresses the danger posed by Sutekh. Early on in the story, as Collins discovers the Doctor and Sarah, we get a fairly typical example of the Doctor's wit, as the butler demands to know how he got into the building; the Doctor cheerfully responds "Through the window. I understood the property was for sale?" However, as soon as the Doctor discovers the nature of his enemy, he is unusually grim throughout, and Tom Baker puts in one of his most intense performances. When the Doctor travels to Egypt to distract Sutekh, he fully expects to die in the process, but throughout the story he gives the impression that he isn't sure that can prevail here. Tellingly, once Sutekh is aged to death in the time corridor, he reverts briefly to his usually cheerful self, just before he and Sarah flee from the burning Priory.
The acting in 'Pyramids of Mars' is very fine throughout. I've already mentioned Micheal Sheard and Gabriel Woolf, but Bernard Archard's performance as the living dead Scarman is very effective, and both Tom Baker and Elizabeth Sladen are on top of their form. Baker is convincingly agonized when Sutekh tortures him and as mentioned puts in a tense performance throughout. Because of this it falls to Sladen to lighten to the atmosphere slightly, which works because it suggests she can't fully comprehend the true danger posed by Sutekh whereas the Doctor can. She also gets to shoot at the gelignite on the ramp of the missile, thus contributing significantly to the Doctor's desperate (and as it happens, failed) gambit to stop Sutekh from destroying the Eye of Horus on Mars.
The Mummies are another highly successful aspect of 'Pyramids of Mars', combining the unstoppable air of the Cybermen in their better outings with a distinctive and creepy appearance; in addition, the weird howling noise made by the Servitor that gets its foot caught in one of Clements' traps is rather spine-tingling. The whole production is very well made, with superb location footage, great sets (I especially like the strange swirling backdrops in the Pyramid of Mars, which creates an alien feel), and evocative incidental music. Overall, 'Pyramids of Mars' is a high point of the generally strong Season Thirteen and a real classic.