'The Deadly Assassin' was apparently rather controversial amongst Doctor Who fans at one time, due to its depiction of the Time Lords as a bunch of silly old fools. It's long since undergone something of a reassessment and is now considered to be something of a classic. Whilst I consider the term classic to be overused by Doctor Who fans on occasion, in this case it is entirely warranted; 'The Deadly Assassin' is a triumph, and works extremely well, despite being rather unusual in a number of respects.
Firstly, I'll discuss the Time Lords. The Time Lords have not been seen to anywhere near the degree that they are used here at any point in the series history prior to 'The Deadly Assassin'. What little we have learned about them paints them as a powerful and technological advanced race; the first story to feature the Time Lords properly is 'The War Games', in which they are shown to be powerful and rather austere. Both the Doctor and the War Chief are clearly afraid of them and they have both the ability and ruthlessness to dematerialize the War Lord and quarantine his home planet. Time Lord technology is often hinted at rather than seen; creating a force field around a planet is no mean feat, and of course the TARDIS itself is a fantastic creation, being as it is both dimensionally transcendental and able to travel anywhere in time and space. In 'Genesis of the Daleks', the Time Lord who appears to the Doctor on Skaro smugly boasts that the Time Lords mastered the technology necessary to interrupt a transmat beam safely when "the universe was less than half its present size", again suggesting considerable technological advancements. In 'The Three Doctors', we see the Time Lords under threat for the first time, and whilst a combination of Roy Purcell's wooden acting and cheap and nasty sets rather undermine them anyway, the fact remains that it takes a being capable of destroying the entire universe in that story to seriously trouble them; significantly, he's also one of their own. Despite that story's considerable shortcomings, it also maintains the image of the Time Lords as a dignified and solemn race.
The other main characteristic of the Time Lords that we already know of is that they have adopted a policy of non-intervention in the affairs of others. They break this on numerous occasions, especially during the Third Doctor's era, when they send him to different alien worlds during his exile, including Uxarieus, Peladon and Solos. But whilst they do therefore interfere, they prefer to do so through an agent provocateur, who of course is often the Doctor; as he says in 'The Brain of Morbius', they get him to do any dirty work that they aren't prepared to touch with their "lily white Time Lord hands". In doing so, they thus further contribute to the aloof air that surrounds them at this point in the series, as they manipulate events from behind the scenes. Faced with the task of writing a story set on Gallifrey, Robert Holmes remains true to all of this, but gives it a brilliant - and rather irreverent - twist. The Time Lords seen briefly in 'The War Games' are ultimately rather dull, so here Holmes takes the amusing option of presenting the Time Lords as politicians, obsessed with ceremony and bound by procedure. The Time Lords of 'The Deadly Assassin' have the trappings of dignity seen in 'The War Games', but we see beneath the surface; the two old Time Lords in Episode One who we see getting changed into their robes are clichéd old men, hard of hearing and grumbling about the young people of today. Hugh Walters' Runcible "the fatuous" is a vain and silly man, entirely consumed by his job of presenting the Public Register Video, a job he carries out with only a modicum of competence and little charisma.
In addition to these rather daft Time Lords we have Borusa and Chancellor Goth, both wily politicians, each intelligent and cunning and each ruthless in his own way. Holmes takes the opportunity to poke fun at politics, mainly through Borusa who gets to utter some wickedly sharp lines such as "if heroes do not exist it is necessary to invent them", and best of all, "we must adjust the truth". Goth is utterly ruthless, more than willing to assassinate the President for his own ends and equally prepared to use the Doctor as a sacrificial lamb, first by helping the Master to frame him and later by hunting him down through the dreamscape in the Matrix. But for all that these two are intelligent and cunning, renegades upstage them both; Goth is foolishly trusting of the Master and it takes the Doctor to uncover the conspiracy that the pair of them have perpetrated. The Doctor's trial showcases this brilliantly, as he sits and draws offensive caricatures of the witnesses before calmly standing up and invoking Article Seventeen, thus taking refuge in the convoluted loop holes of Gallifreyan law, which Goth is forced to accept in public. Unusually for a Robert Holmes story, a character who is essentially a policeman proves to be the Doctor's greatest ally; the plain speaking Castellan Spandrell approaches politics with cynicism and quickly realises that the Doctor is telling him the truth in Episode Two. This then, is how Holmes approaches the grandeur of the Time Lords: by revealing it to be a sham, a hollow veneer of pomp and ceremony beneath. Even the Chancellery Guards, splendid though they look, are supported by a veneer of ceremonial armour, beneath which they are shown to be incompetent, the Doctor and the Master both running rings around them.
If the Time Lords are thus portrayed however, it raises the question of how this meshes with their reputation as technologically advanced manipulators. The latter point is brilliantly accounted for by a throwaway reference to the Celestial Intervention Agency, an organisation so secretive that even the Castellan is not privy to their secrets. With this one line, Holmes is able to convincingly present us with his rather unfaltering portrait of the High Council, whilst still allowing for the interventionists seen in stories such as 'Colony in Space'. The second point is even more brilliantly realized, as it becomes clear that whilst the Time Lords are indeed possessed of incredibly advanced technology, they can't actually remember how most of it works. The Eye of Harmony, the power source for their entire society, has passed into legend to such an extent that Spandrell thinks it is a myth and that if it did once exist it doesn't any more. The tools Rassilon (mentioned for the first time in 'The Deadly Assassin') built to control the power of the Eye have been reduced to the status of mere ceremonial relics, symbols of power but with no known function. Even the potential of the Amplified Panatropic Net, used to predict the future, is not fully realized until the Master makes use of it. Co-ordinator Engin, who maintains the Matrix equipment, is in awe of it rather than understanding it; he simply cannot believe that anyone could interfere with it in the way that the Master does. Thus, we do indeed see the technology hinted at in previous Doctor Who stories, but Time Lord society has become so stagnant and apathetic that most of it has fallen into disuse.
Another noteworthy aspect of 'The Deadly Assassin' is of course the return of the Master. Rather than simply recasting the late lamented Roger Delgado and introducing a new incarnation, Holmes and Hinchcliffe choose instead to reduce the Master to the status of a walking cadaver, hideously disfigured and both literally and physically near to death. Peter Pratt's Master is twisted in both body and mind, and whilst he's true to the character established during the Pertwee era, he's also dramatically changed, his characteristic charm literally seared away along with his distinguished, if rather devilish, looks. This corpse-like Master fits perfectly into the gothic horror of the Hinchcliffe era, alongside such memorable villains as Davros and Morbius, and with his skull-like visage and his billowing black cloak he inevitably, and strikingly, resembles the Grim Reaper. Ironically, in bringing the Master this close to death, the production team also gives his character a new lease of life. Whereas the Master of old was motivated by power and a desire to humiliate the Doctor, his motivation has now changed; he still wants revenge against his old enemy more than anything (he notes on two occasions that hatred keeps him alive), but his primary motivation now is to survive, a drive so overwhelming that he is willing to destroy both Gallifrey and the Time Lords in order to succeed. Whereas in the past the Master occasionally seemed more interested in his rivalry with the Doctor than actual victory, and could therefore often be reasoned with, his new status brings with it a desperation that makes him far more ruthless and dangerous than before. 'The Deadly Assassin' would have worked perfectly well as a final story for the Master; brought to such a state and clearly dying, the Master could quite easily have been permanently written out of the series at this point. Instead, Holmes gives him a new slant and then sends him on his way, temporarily revitalized by the Eye of Harmony and escaping in his TARDIS at the end. As a means of reintroducing an old and popular enemy, it works very well and gives a tantalizing promise of a rematch in the future.
In terms of structure, 'The Deadly Assassin' is highly unusual. Episode Three is rightly famous, set almost entirely in the Matrix and consisting as it does of a long battle between the Doctor and Goth, with a plethora of surreal and impressive imagery and making great use of the location filming. With very little dialogue, the episode is an intense twenty-five minutes as the Doctor struggles to survive, and this means that whereas Episode Three of a four part Doctor Who story is often reserved for an explanation of the plot, here that takes place at the start of Episode Four. Episode Three is so well directed and so well paced that it never once feels padded and passes at break-neck speed, and the notorious final shot of the Doctor's head being held under water by Goth is highly effective. However, it is also worth mentioning Episode One. 'The Deadly Assassin' is unique because it is the only Doctor Who story in which the Doctor is unaccompanied by a companion, and this results in a first episode in which the Doctor is entirely on his own, desperately trying to evade capture as he strives to save the life of the President. After the equally unusual voice-over introduction with caption, this results in a fast paced and adrenaline charged episode that is just as worthy of recognition as Episode Three.
In production terms 'The Deadly Assassin' is flawless. The green-tinted sets of the Capitol look old but dusty, reflecting the sense of stagnation prevalent in Time Lord society, and amidst this faded splendor the colourful Time Lord robes with their distinctive collars look entirely appropriate. The ominous but slightly pompous musical score also perfectly suits the story, and David Maloney's superb direction brings everything together perfectly. The acting is uniformly excellent, with Erik Chitty's doddery and absent minded but thoroughly likeable Engin forming a classic "Robert Holmes double-act" with George Pravda's caustic Spandrell (making amends for his atrocious performance as Jaeger in 'The Mutants'). The ever-reliable Bernard Horsfall is perfect as Goth, bringing the necessary dignity to the character in Episode One, but also having the physical presence to convey menace as he hunts the Doctor in the Matrix. Entirely obscured by his costume, Peter Pratt does wonders with his voice alone, bringing some of the Master's old charisma to the role but also sounding suitably ghoulish. But for me Angus Mackay as Cardinal Borusa, bringing to the role dignity, presence and dry wit, steals the show; his casual dismissal of Runcible is hilarious, but best of all is his final scene with the Doctor, as he first utters the withering line "you will never amount to anything in the universe whilst you retain your propensity for vulgar facetiousness", and then follows it up with the wry "nine out of ten", briefly hinting at real affection for his old and wayward pupil. It's a marvellous performance in a superb story and is just one of the many reasons that 'The Deadly Assassin' is a true classic.