Doctor Who's biggest continuity error is the origin of the Daleks - but there may be a simple way to fix it. When Doctor Who began in 1963, the BBC no idea what it was destined to become. In fact, it started off as more of a historical series than a sci-fi, with showrunner Sydney Newman disliking the prospect of using "bug-eyed monsters" and alien creatures like the Daleks.
There was little interest in continuity in those early years. Every story was expected to stand on its own two feet, and the BBC didn't expect anyone to ever re-watch an episode; in fact, they routinely wiped the tapes, erasing their copies of stories from the William Hartnell and Patrick Troughton eras. It wasn't until the 1970s that the BBC began to even understand there was a small core group of fans who were interested in continuity, which led to a series of episode guides, but these were considered to be a small minority.
Unfortunately, this inattention shows, and as a result the early Doctor Who stories frequently contradicted one another. This was true even as regards some of the central tenets of the show, such as the concept of regeneration. But there's no more egregious an example than the origin story of the Daleks - because Doctor Who told that story twice.
The Two Histories Of The Daleks
The Daleks were created by Terry Nation in 1963, in a story originally called "The Mutants" and now understandably referred to as "The Daleks." The script was commissioned by script editor David Whitaker, who was impressed with Nation's previous work. Newman wasn't keen on the approach, but other scripts fell through, and in the end "The Mutants" was the only one finished. By the time the seven-episode tale had come to an end, Doctor Who was completely redefined as a science-fiction classic.
The plot saw the TARDIS land on the distant planet of Skaro, and the Doctor sabotaged his own vessel in order to stick around and explore the alien world. The TARDIS crew discovered that Skaro was inhabited by two races, the Thals and the Daleks, who had become locked in a Neutronic War. The planet had been flooded with radiation, rendering it almost uninhabitable. The survivors of the Thals had fled into the mountains, where they had become pacifists. The Daleks, meanwhile, had refused to be driven out of their city. They had mutated into hideous post-human forms as a result of the Neutronic radiation, and had created the classic Dalek shells as travel machines. When the Daleks learned that the Thals were still alive, they dedicated themselves to exterminating them. Fortunately, these first Daleks were entirely dependent on their connection to a powerful generator, which the Doctor deactivated.
The Daleks became an instant hit, inspiring a popular craze in Britain known as "Dalekmania." It didn't take long for the BBC to see the aliens' potential, and by the end of the 1960s the Daleks had appeared in two movie adaptations. The origin of the Daleks was fleshed out in a popular TV Century 21 comic strip, which introduced a scientist called Yarvelling who was responsible for creating the distinctive Dalek casing. Meanwhile, the Daleks became Doctor Who's greatest threat, a recurring nemesis.
And then, in 1975, showrunner Barry Letts and script editor Terrance Dicks commissioned Terry Nation to write another Dalek origin story. The result was "Genesis of the Daleks," widely considered one of the best Doctor Who stories of all time, in which Tom Baker's Fourth Doctor was sent back to the Daleks' origin by the Time Lords. He was charged with averting it - but he only succeeded in delaying it. "Genesis of the Daleks" introduced the Kaled scientist Davros, creator of the Daleks, an insane cripple with a sociopathic desire to create the supreme race. The Nazi comparisons became overt, with Davros' Kaled allies wearing uniforms reminiscent of the SS.
The broad brush-strokes of "Genesis of the Daleks" are the same as "The Mutants." There are still two races struggling to coexist on the same world, caught up in an escalating war that's going nuclear - or, rather, Neutronic. But the details are different, because in "Genesis of the Daleks" the Daleks are created before the Neutronic bombs begin to fall. Davros had foretold the coming mutation, and indeed accelerated it, going on to create the Daleks' distinctive travel machines.
Is There Any Way To Solve The Daleks' Continuity Problem?
These two accounts are quite difficult to reconcile, although matters are simplified by discounting the more detailed version of the Daleks' origin detailed in comic strip form; there's no real evidence that should be considered canon in the first place. With that issue resolved, it's actually possible to pull the continuity threads together by using a more modern conceit.
In 2005, Russell T. Davies relaunched Doctor Who. This modern Doctor Who was set in the aftermath of a great "Time War" between the Daleks and the Time Lords, in which the races had brought one another to the brink of ruin in a battle that broke the laws of time and space. The Time War is naturally a useful concept for explaining away continuity problems - and that's particularly the case for the Daleks. Indeed, Davies envisioned "Genesis of the Daleks" as the beginning of the Time War, with the Time Lords using the Doctor in an attempt to erase the Daleks from history.
This raises the possibility that there are two Dalek timelines, not just one; the original timeline, and the one initiated by "Genesis of the Daleks." Perhaps in the first timeline, Davros' experiments ended in failure when his bunker was destroyed by one of the Neutron bombs; the Kaled survivors realized they were mutating as he had predicted, and thus sought out his travel machines. In the post-"Genesis" timeline, though, Davros' Daleks survived beneath the rubble of the bunker, and emerged as the primary Dalek race.
Doctor Who has frequently suggested that time tends to correct itself, and as a result the Doctor's actions in "Genesis of the Daleks" don't seem to have had much of an impact. The Doctor believed he'd delayed the Daleks' rise as a galactic power by a few thousand years, but if so, they rose to exactly the same position of dominance. By the 22nd century, the timelines had essentially converged once again; that explains why both timelines saw the Daleks successfully conquer Earth in that time period, as detailed in Doctor Who episodes "The Dalek Invasion Of Earth" and "The Five Doctors." It seems the Time War was inevitable - no matter how hard the Time Lords tried to prevent it.