A Titan Comics tie-in explains the real origin of Doctor Who's "Timey-wimey" catchphrase. Time travel is hard, and precious few franchises handle it consistently. In part, that's because time travel is purely theoretical, with no real-world analogue, and as a result every film and TV series that deals with it has to develop their own rules. Quite rightly, these rules are meant to be broken, because these are stories, not essays in temporal physics.
The longest-running science-fiction TV series in the world, Doctor Who has been dabbling with time travel since 1963. It's usually used as a plot device, explaining how the Doctor wanders between different worlds and time periods, but every now and again a story shines a light on the temporal mechanics. Rather than give the audiences a lecture, the writers have developed a simple shorthand for these temporal mechanics, with the Doctor offhandedly dismissing things as being a bit "timey-wimey." The phrase was apparently coined by David Tennant's Tenth Doctor in the classic episode "Blink," and in "The Day of the Doctor" Matt Smith used it as well - much to the disgust of John Hurt's War Doctor.
However, according to Titan Comics' The Third Doctor miniseries, the Doctor didn't come up with the expression at all. Instead, it seems it was created by the Third Doctor's companion Jo Grant in the aftermath of "The Three Doctors," as she attempted to understand how multiple incarnations of the Doctor could interact with one another. Anyone familiar with the Jon Pertwee era will be unable to resist a smile at this revelation, because it's perfectly in-character for Jo. Presumably John Hurt's War Doctor had become so embroiled in the darkness of the Time War that he had forgotten such an innocent phrase.
The Third Doctor miniseries presents itself as another multi-Doctor story, with the Second Doctor unexpectedly turning up. As the Doctor explains, in general it seems Time Lords forget such encounters until they've happened for all the affected incarnations, explaining why multi-Doctor stories can happen in the first place. In an ironic twist, Paul Cornell's script turns that idea on its head, because in reality this isn't the Second Doctor at all - it's an imposter, deceiving the Doctor in order to gain access to the TARDIS.
Of course, this has profound implications for Doctor Who season 12, in which Jodie Whittaker's Thirteenth Doctor encountered Timeless Child retcon. Unless, of course, there's something else Jo Grant would describe as "timey-wimey" going on.