Theory:Doctor Who television discontinuity and plot holes/Silver Nemesis


 * The Cybermen know of Lady Peinforte but they have never encountered her before. How they know of her is unclear.
 * If they know about the Nemesis, they may know of her role in its creation.


 * How do De Flores and Karl overpower the Cybermen in the mausoleum, and why does Karl go through the seemingly pointless feint of betraying De Flores in the first place?
 * Since the Cybermen evidently believed Karl was on their side, they probably left only one to guard De Flores while the rest attended more urgent matters. The "seemingly pointless feint" was because they were hopelessly outnumbered by Cybermen. It certainly bought them enough time to get away.


 * Lady Peinforte's arrows are made of gold, so apart from fighting Cybermen, they're the most useless arrows ever created. (Although they may have been intended to kill with their poisoned tips rather than impact alone.)
 * Gold might not be as hard as other metals, but if it hits an unarmoured person, it would still penetrate.


 * First the hardness depends on the purity / percentage of gold in the arrowhead. But it's also possible that for the arrows to remain effective, the arrowhead is simply gold-plated instead of solid gold.


 * There's a few cases of people standing about doing nothing for no real reason:
 * Firstly, when the Doctor and Ace get the bow to the statue, none of the Cybermen do anything to stop them (Some of them even blatantly ignore a direct order to kill them, one for seemingly no more logical reason than the Doctor having used his cybergun as a hat-stand).
 * Ever heard the phrase 'bulls#!t baffles brains'. The Doctor clearly has, and that's exactly how he confounded the Cybermen.


 * Secondly, De Flores had the bow at the statue, the Doctor makes no attempt to stop him and has to rely on the Cyberleader to kill him.
 * For your second point, the Doctor is keeping De Flores talking so he doesn't know about the leader. This fits in with his manipulative personality.


 * Considering how the Doctor willingly handed the bow over to the Cyberleader a short while later, clearly it was no longer that important.


 * Thirdly, Lady Peinforte makes no attempt to stop the Cyberleader getting the bow, or to take it from the Doctor. (Perhaps Lady Peinforte thought herself outmatched and thought it would have been useless to fight the Cyberleader or Doctor.)
 * For the third case, you've answered your own question.


 * What exactly should she have done? Don't forget that she seemed to be somewhat on the thin edge of sanity.


 * Finally, the Cyberleader stands perfectly still, waiting for Peinforte's servant to stab him with the arrow.
 * Cybermen are notoriously logical and perhaps when the Cyberleader saw the arrow, it though there was no reason to fight and it would have been too slow to run.


 * His attention was focused on the Doctor, whom he was about to kill. Richard's reactions were evidently too quick for the Cyberleader.


 * How is that arrow still in the TARDIS door anyway? The Doctor removed it when talking to Ace about the Nemesis, and the TARDIS materialisation is seen several times with no arrow in it.
 * Considering the number of traps the Doctor has placed is it unreasonable to assume he put it back there so that Richard would kill the Cyberleader?


 * On the contrary, the Doctor takes a close look at the arrow but clearly leaves it there.


 * Why did Peinforte wait till the Doctor and Ace were in the TARDIS before firing the arrow in the first place?
 * The Doctor recognized the gold tip as "Lady Peinforte's calling card", so perhaps the arrow was meant as a warning not to cross her.


 * At the end of this story, the Doctor seems to have completely overlooked the fact that Richard was, at the least, a willing accomplice to the cold-blooded murder of the mathematician.
 * The Doctor is not a policeman. And don't forget that Richard had just saved his life.


 * It's never explained why the two controlled humans shoot at the Doctor and Ace in the first episode (this incarnation, after all, is unknown to the Cybermen).
 * Cybermen display the ability to recognise the Doctor, regardless of incarnation, in Earthshock. There's no reason to assume they didn't scan the Seventh Doctor offscreen and determine he was likely a different form of the same being.


 * David Banks' eyes are visible as the Cyberleader pulls the coin out in episode three.
 * Visible Cyberman eyes, however, were a feature of the earliest costumes, and may have been intended to imply some remaining organic matter. In "Earthshock", it was certainly suggested by the transparent chin-guards on the Cyber helmets that some of the humanoid head was still preserved within the armour, and "Silver Nemesis" appears to have reverted to that design (albeit with grilles added to the chins).


 * Slightly more bemusing is the fact that the Nemesis statue, with its inadequately-shaded eyes, clearly blinks as it is activated (Curious behaviour for a solid lump of metal, albeit living).


 * Why don't Ace's coins bounce off rather than pierce the Cybermen?


 * Why doesn't Peinforte and Richard's arrival draw some sort of response from the people in the café?
 * The people on their left (and the only customers in shot) actually do react, yet they do this inaudibly and sit still in their places.


 * It has been stated that it would be impossible for anyone from 1638 to calculate correctly a day 350 years later as in 1752 the Julian calendar was 'brought into line' with the Gregorian one (effectively meaning that 11 days from 3 to 13 September were skipped over).
 * Peinforte's time travelling is caused not by her own ingenuity but by Fenric.


 * At about 6 minutes into episode two, back in Lady Peinforte's home, the Doctor retrieves a note and burns it. He tells Ace that although the mathematician was a genius, he did need a nudge in the right direction. The content of the note is unknown, so it could very well be an in-story explanation for how the mathematician resolved the discrepancy. Considering the Doctor's recent penchant for elaborate and intricate schemes, it would be no surprise if he had provided the crucial information to ensure that Lady Peinforte would travel to the correct time. However, there's no confirmation whether the Doctor authored the note, and finding it may simply have filled in a puzzle piece for him.


 * In previous stories the Cybermen could only be killed by gold if it was ground into their chests, clogging their breathing apparatus', not by the mere touch of it. How have they got so weak to it all of a sudden?
 * The gold doesn't merely 'touch' them, it's inserted forcefully, either as the tip of an arrow, or a gold coin flung by sling shot. Furthermore, their respiratory units seem to have been redesigned for the worse, lacking the protective grilles from "Earthshock" that would only admit small particles of gold. Perhaps they have been forced to downgrade from lack of resources, owing to their increasing catalogue of defeats. However, the gold-related deaths in this serial do contradict the explanation given by the Doctor in "Revenge of the Cyberman", that gold kills Cybermen by clogging up their breathing mechanisms. The effect shown in "Silver Nemesis" is quite different, the gold projectiles causing a rapid death with electrical sparking, rather than the protracted suffocation (with no such sparking) that had been shown in previous stories.


 * The design of the Cybermen in this story is too advanced for the time period it is set in. See the Cybermen in "The Tenth Planet", and "The Invasion." The Cybermen here more resemble the ones from "Earthshock" and "Attack of the Cybermen."
 * The Cybermen clearly do not have a linear progression; either they've branched out in different directions, or they have more time travel than we know about. David Banks' book Cybermen makes a go at the first type of explanation (which it looks like this wiki treats it as canonical), and it pretty much all works, but it's far too much information to fit into an answer here.


 * Also, the fact that the costume design is more advanced doesn't necessarily mean that they're more advanced in-universe, just that the show has improved (or just changed) the way they represent Cybermen (in the same way that the fact that the Cybermen are actually played by human actors in costumes in the BBC episodes doesn't mean that in-universe they're actually human actors in costumes).