WARNING! THERE MAY BE UNMARKED SPOILERS!
It's a metaphysical question
The title will be the start of a discussion concerning Fixed Points.- Jossed
It isn't
There are filming shots showing WW2 Germany.- Confirmed
It's both
Taking the themes of Genesis of the Daleks and sticking them in their historical inspiration.- Jossed
Hitler is going to be Melody's first target.
"A significant factor in Hilter's rise to power is that the Doctor didn't stop him."- Semi-confirmed. That was Melody's plan, it just didn't succeed.
It's at the end of the war
They kill Hitler on April 30th 1945, everyone just assumed it was suicide.- Semi-confirmed. This is the Justice Vehicle's usual M.O. but they came early.
Winston Churchill will appear in the episode.
Hitler and Churchill never met in real life, it's time to throw history to the wind and have some awesome showdowns. Also, the Doctor will compliment Winston's bowtie.- Jossed
It's going to be about fixed points in time
Amy's mantra is 'Time can be rewritten,'. Amy and Rory are going to want to get baby Melody back, but that's impossible as it will create endless paradoxes involving little girl!Melody (especially during the events in Impossible Astronaut/Day of the Moon) and grown up Melody/River Song. The Doctor will have to demonstrate to the Ponds how you can't change timelines by screwing with Fixed Points in time, and will do so by showing them the most famous fixed point of all: Hitler. Hitler really sounds like someone who would be on The Doctor's hit list. Genocide? check. Trying to rule the world? check. Trying to rewrite history (in a sort of mundane, textbook way) check. Evil army of normal people 'just following orders?' check. So why hasn't the Doctor gotten rid of him already? Fixed Point in Time. Can't do it.- Confirmed - But in a round-about manner: The Tesselecta takes targets shortly before their death and replaces them with copies in order to avert paradoxes. However, they came too early for Hitler, and it is never stated if his alleged suicide in 1945 is a Fixed Point or not. At the same time, The Doctor's death at the lake in Utah is explicitly stated to be a fixed point in time.
The Silence are behind it in some way
WW2 accelerated/caused the space race and eventual moon-landing... and we know how well that turned out for them. So now they're trying to avert it.This is the episode when we finely found out how the Valeyard came to be
The Valeyard is the living personification of the Doctor's dark side. For all we know, this is the episode where he is "born." The 12th Doctor could be when he becomes an Enemy Without.Here, the Doctor somehow snaps and does something REALLY bad( with Hilter and history thrown in) then the Valeyard is born in the end The Doctor is turned back to normal(or normal as The Doctor can get) but the Valeyard is now his own person and runs off to get Sixth in...The Mysterious Planet.- Jossed
River kills Rory.
She killed "a very good man", and this isn't the first time the show tried to trick people into thinking a character's referring to the Doctor when they're actually referring to Rory.- Jossed
Hitler will die, and bad things will happen.
The story is about fixed points in time, and this story will show the effects of defying time. In this case, by killing Hitler It could invole either one of the Doctor's companions(they don't know about fixed points yet), or the Doctor himself(in a toned down version of his Time Lord Victorious attitude). What effects this will have on the timeline won't be the obvious "Nazis rule the world," but it will still be very bad.- Jossed
They accidently save Hitler
Thus seriously raising the question as to if WW2 as we know it is a fixed point in time.- Confirmed. They have crashed the TARDIS into Hitler's office while a robot was attempting to assassinate him.
The Silence's Question is...
Doctor Who?. Moffat likes the mystery of the Doctor's real name, after all, and River knows/knew/will know it. It's the oldest question in the series. Also, that question has been answered- not to us, naturally, but to River and, no form of Silence has yet Fallen as a result. Then again, Timey Wimey, so who knows? The records did say the question is in plain sight. What's plainer than the title of the show we're watching?- "What is the Matrix?" Just Rule of Funny.
- Confirmed
The Doctor whispered his name to River
He was on the verge of dying (again), so maybe this is the "only time [he] could" tell someone? This may link the whole wibbley mess of River, the Silence, and the Doctor's other death from this season together (up to and including why River's first episode was called "Silence in the Library"). "I'm sure she knows" could easily make sense as "if you're that close I'm sure she knows your name". Rory is The Master
The banging in his head wasn't Hitler. The Teselecta Crew were Jack Ruby, and killed Lee Harvey Oswald.
Originally Lee Harvey Oswald survived and was either found innocent or somehow escaped justice. The Teselecta tried to confront him for his assassination, but bungled it and killed him. Alternatively, they're the man in the white hat and wasn't able to get there in time. The ambiguity didn't help. This episode affected the timing of World War II, and some of Hitler's actions.
From Adolf Hitler's point of view, three British-looking figures invaded his headquarters and locked him in a cupboard. Germany would've gone to war anyway, but Hitler chose to do so earlier because he was paranoid about the British due to the time travel incident. This may have also motivated some of the Blitz. His increased paranoia, ego and madness as the war continued were in part due to his humiliation by the Doctor and friends wounding his pride. The reason the Doctor doesn't take Hitler seriously.
It's not just for comedic purposes, but in the grand scheme of things he's far from the worst person the Doctor has encountered. Even going by just individuals he's witnessed planet-wide genocide. Hell, as far as he knows he's killed far more people than Hitler ever will and ever did through the Time War. Obviously he considers the Fuhrer a despicable human being, but having faced a lot worse is content to simply have him humiliated and locked away for now.