The first four episodes have already been filmed while episodes five and six (a two-parter) were shot over the past month. The seventh episode, a cliffhanger finale until the second batch of six episodes in the Fall, begins shooting early in the new year.
Much of the trailer shows scenes from the Steven Moffat-penned opening two-parter set in the 60's in the United States. These include The Doctor in the White House, the various scenes in Monument Valley and shots of a bearded Doctor being held prisoner in Area 51. Seems like the legendary 'Men in Black' play a big part of the storyline here, as does Alex Kingston's Dr. River Song.
Various scenes show the main characters with tally marks on their skin. The various actors were spotted wearing these marks during filming in Utah so they definitely show up in the season premiere.
Shots of someone in a full astronaut suit, and River Song likely distracting someone with an eyeful of her naked body, are both said to be from the opening two-parter.
The Silence, the threat that caused the TARDIS explosion and the resulting cracks in the universe last season, will be a running thread throughout this season and are seen in the opening two-parter. Apparently it's a 'them', not an individual, and likely a race hereto unseen in the Who Universe. It's also been said that the truth about their "needs" and "physical forms" are what's sinister about them.
There's several shots from Neil Gaiman's episode (the third episode next season) set in an alien junkyard with a woman in an 18th century dress and hairstyle. Its been stated the woman in the junkyard, Idris, is someone the Doctor has met before onscreen who looks different now.
The TARDIS knock-off seen in "The Lodger" episode last season seems to have returned as there's a shot of River Song exploring it with a flashlight. There's also shots of a green-eyed Ood, Amy and Rory in some kind of dark spaceship corridors which are rumoured to be part of a TARDIS.
The third episode is also said to tie into the classic Second Doctor episode "The War Games" in which the various warriors from the history of not just our planet were brought together in a 'battle royale' of sorts. Shots early on in the trailer of three men dressed like Musketeers and a shot of Nazi soldiers are said to be from this episode and lend credence to that theory.
There's shots of small blond people in very creepy doll masks. These are all likely from the Mark Gatiss-penned fourth episode.
The Doctor apparently gets cloned in the fifth & sixth episode two-parter in a story that deals with an alien invasion.
It has been confirmed that Amy is "harbouring a big secret", and that the episode 7 finale will reveal the "true nature of his [The Doctor's] relationship with Amy Pond" says Moffat.
That ties in with rumours of a scene in the opening two-parter that Amy encounters a "future Doctor" (possibly the one with the beard) and learns from him something terrible that will happen to The Doctor in the future, something that River implores her to keep quiet.