I found this channel on dailymotion with Classic Who episodes with English subtitles. I tried one (because the episodes' titles were in German, so I half expected German dubbing instead of promised subtitles - not that I know whether the Classics have ever been released in Germany), the one called The Brain of Morbius. Beside my brain associating it with Möbius, the story is famous for claiming William Hartnell's regeneration wasn't the Doctor's first, so I wanted to watch it.
It's true. When the (Tom Baker's) Doctor has a sort of mental fight with Morbius, we see the Doctor's three previous faces, from Jon to William, and then some more faces (easter egg: some of them being Doctor Who writers and other people involved with the series, because well, who could resist making yourself or your friend the Doctor?), and Morbius asks: "How long have you lived, Doctor?". The implication is clear: all those faces are the Doctor's and the body we saw in "The Unearthly Child" is about his seventh or eighth regeneration. But everyone just ignores that. The viewers never bought it, while other fact that, as I read, was stated only once in the entire Classic Who - the fact that the Doctor can regenerate only 12 times - has been carved in our brains so deeply that thirty years later, Moffat had to come up with "a new set of regenerations" when the Doctor ran out of them. It only proves how selective we are in absorbing "facts" about a fictional universe; we only take what we feel it's good for the story we already have in our heads. We decided the Doctor is a better character when he's mortal, hence the limit. We decided we don't want any off-screen regenerations. We decided the Doctor is better as an alien, not half-human, and most of us call him the Doctor, not Doctor Who. Anything stated in the series can be changed, reseted or just ignored. With that in mind, I wonder what people will be saying about the Doctor destroying/not destroying Galiffrey in ten years. Right now, the feelings about what is better for the story vary.
So - don't overestimate the importance of continuity. Just because something was said once (or even more times), it doesn't necessarily mean it got into our brains. That's the beauty, we create that Doctor Who myth in our heads ourselves so writers can try to come up with something interesting without worries about breaking the whole series. Seriously, who "believes" the TARDIS makes the noise because of the hand brake?
I knew about the Doctor's faces, but I didn't know the story would be set on Karn. I was sure there was Karn in Classic Who, because I learnt if there's something in the new episodes that seem weird or out of nowhere but it's just accepted, the explanation is somewhere in the Classics. The same goes with the Sisterhood of Karn and their elixir that triggers Time Lords' regeneration. There's a weird thing - you start watching the series thinking Time Lords is just a species, and an extra heart and regeneration are natural for them just like one heart and an ability to heal a broken bone are to us. Only then you learn that you're not born a Time Lord, you become one, an extra heart is because of something, regeneration comes from the elixir, and blah blah blah, basically everything about Time Lords is artificial. It makes them less powerful, they're just a random race that achieved power and you start to wonder what they were like when they were still developing and evolving. Maybe those times are more interesting than those when they're just collars standing proudly in the sun. Maybe if the Doctor was born earlier, he'd be happy on his home planet?