It was not one of the best Doctor Who Christmas specials, but this year's did have an interesting concept at play: dreams within dreams where the characters believed they were dealing with real time, interactive events, even though they were not even in the same location.
In LOST, dream theorists believe that the characters were all hooked up on machines that criss-cross neuron-impulses to create a fabricated, collective dream matrix. It is run by the subconscious mind, like running through levels of a video game. Nothing is real, even though your brain and your senses think it is real.
But the application of dreams within dreams can explain the problematic sideways universe. In essence, the characters mental comas or sleep states could have created the following layers: background stories; the flight from Sydney; the crash onto the island; the island events; the off-island events like the O6; the inconsistent time travel events; and the sideways world. Even when someone died on the island, like Libby, she was still an illusion in the next layer of the complex dream state: the sideways arc.
The dream state explanation is one of the true unified theories to LOST. Since dreams are not reality, basic tenets of fact like time and physics (such as a moving island) do not matter so there is no continuity errors. Vivid dreams can take the place of actual events in minds that are broken, drugged or fragmented - - - which are traits in most of the characters who landed on the island.