This story follows on from the very moment Logopolis ends (indeed, we get the regeneration as a pre-credits sequence) - yet the location appears to have totally changed (as have all the security guards).
We've been told that the Pharos Project is in Cambridgeshire - yet the ambulance which turns up has come all the way from East Sussex, just over 100 miles distant.
Who called the ambulance in the first place? We see it, but no police cars. If the incident is one of trespassers then there ought to be police cars, not ambulances.
If called because the Doctor was seen to fall then that's impossibly quick. (It can't have been called for the technician who was knocked out earlier, as it would have gone to the building where he was injured and not way over where the Doctor fell).
The Fourth Doctor fell off the telescope wearing boots and the Fifth gets up in the exact same clothing - but is now wearing shoes. We've seen the Doctor's outfits change during regeneration before (the First to Second) but then they changed significantly, not just a single item.
As with the last story, if the Master has a fully functioning TARDIS, including its chameleon circuit, why does it appear as a classical column in the middle of a piece of waste ground in 1981?
And another knock-on from Logopolis: when exactly did the Master came up with the plan to use Block Transfer Computations - which he's only just learned about - to set up two different traps for the Doctor.
He couldn't have known he was going to be able to capture a mathematical boy-genius, yet within seconds he not only has a copy of him to infiltrate the TARDIS and send it to Event One, but also gets the whole Castrovalva trap set up within minutes of that failing.
Why would someone who regards himself as a criminal genius have back-up plans in the first place? Shouldn't he be so confident of his abilities that his initial plans cannot ever possibly fail?
If Block Transfer Computations can manipulate matter, why does the Master not use it ever again, or as a simpler method of killing the Doctor, like making a piano materialise above his head? He may have lost Adric but there are other mathematical experts around whom he could exploit.
Why has the Zero Room never been mentioned before? Surely it would have helped the Second, Third and Fourth Doctors recover from their regenerations.
When we see the Doctor levitate, the question mark on his shirt collar reverses - as does his hair parting.
Why does no-one comment on his telepathic communication with Tegan and Nyssa, which he hasn't demonstrated before? His lips don't move when he speaks. Is this supposed to be telepathy, or just bad dubbing?
If the Zero Room really is totally cut-off from the external world as the Doctor says, how can a mathematical projection of Adric be projected into it?
Tegan's handbag mysteriously shifts from the Cloister Room where she left it in the last story, to the console room.
We are told in Part Two that Event One is the beginning of the Galaxy. It is the theorised beginning of the Universe. Galaxies aren't created in the same way.
Anthony Ainley wears a decent make-up as the Portreeve, but you do wonder why the Doctor - recent regeneration or not - can't recognise him.
