There's a bushel of spoilers, following on from last night's premiere. Let's see... The opening episode is described as "Independence Day on the village green." The new TARDIS console "looks like it has been constructed from items out of a junk shop, including an old typewriter, a telephone, pressure gauges and a Morse code machine." The first episode's villain is indeed a shape-shifting alien.
Steven Moffat says, "At the end of the last story, the Tardis was exploding, so it rebuilds itself around the new Doctor. And because the Doctor is completely mad, it builds itself around his madness." It has hexagonal and circular "roundlets" built into the concrete and bronze walls, and besides the aforementioned three levels, there's a door leading to other rooms. And the junk on the console includes a gramophone speaker, a petrol pump, dials and pistons. The word "steampunk" is used.
The TARDIS, crashing to Earth in the 1990s, nearly hits Big Ben. The little girl he meets after it crashes is named Amelia Pond, and she asks, "Who are you?", hoping that he's come to fix the crack in her wall. Replies the newly regenerated Doctor, "I'm the Doctor. Don't ask stupid questions and do everything I tell you." His main priority is eating as much food as possible. Then the Doctor vanishes and reappears 12 years later, when Amelia (now Amy) is a kiss-o-gram dressed as a policewoman. And it turns out the crack in the wall that young Amy was worried about was actually a doorway to a prison that held a villain, whose escape leads the Atraxi to declare they'll incinerate all human life. There are just 20 minutes left to save the world. At one point in the first episode, the Doctor actually says, "Who da man?"
For the rough cut of episode one, at least, the show still had the same title sequence, only with a different font and a new logo. Matt Smith says "Geronimo" again, early in the episode. And the story is the weakest part of the first episode, which mostly focuses on the main characters. But it's still a great beginning, with some funny one-liners.
The newly regenerated Doctor's first words to Amy are to demand some food item, that's all he can think about. One character asks Santa to send them something unusual. Amy Pond's handy with a cricket bat. The TARDIS swimming pool and library are mentioned. Some familiar faces, previously seen on the show, make cameos, plus Patrick Moore, who thinks Amy's grandma is a fox. People refer to the Doctor as "raggedy," "magic" and "a disappointment." The Doctor commandeers a laptop to save the world using Twitter (!) and comes across something inappropriate. A fire engine turns into an unconventional rescue vehicle. The Shadow Proclamation is mentioned. The Doctor "bares all" to Amy.