Idea Proposed and Not Used During the JNT Era: The Doctor's Wife. Look, JNT was just baiting the press with that one, stop taking it seriously.
Central Premise Recycled From: "Edge of Destruction." No, really, think about it. Also quirky malevolent aliens naming themselves after family members is straight out of "The Family of Blood."
Reference to Moffat's Back Catalogue: Doctor having romantic relationship with woman who Understands Him Like No One Else Does, but is doomed, and gets his companions out of the way to do it. Rory makes yet another reference to his now-nonexistant life as a Nestene. Also, from this season (already), companions going all timey-wimey and graffitiing messages as a consequence.
Amy Saves the day with Wuv: Actually the theme this year seems increasingly to be Amy Failing to Save the Day with Wuv, as the incident with Rory aging to death seems to indicate that Rory's got a few abandonment issues.
Joss Whedon Called...: He wants his patchwork people made out of bits of demons/aliens back.
And from Lawrence Miles: The TARDIS is a human girl. Plus Idris says "it's About Time" at one point.
Murray Goldwatch: The "Da-da-da, da-da-da-da-da" theme comes in about 26 minutes in, and we also get some Carmina-Burana-by-way-of-The-Phantom-Menace choir action during the running around corridors.
Nostalgia UK: Neil Gaiman counts, unfortunately. But apparently Tardis consoles include a "retroscope."
Inside Jokes: The Doctor's Wife, and "it's About Time!" see above. The episode starts off with what sounds like a reference to "The Androids of Tara," but it turns out to be a fake-out. The Doctor asserting that he's rebuilt the console before is probably a Pertwee Era reference. There's a shaving mirror on the jury-rigged console, and a reference to the Eye of Orion as a holiday spot. Idris' babble is taken from Dalek Sec, which is itself taken from Ghost Light (which is a clear massive influence on this story). The original Celestial Toymaker story featured a malevolent Aunt and Uncle. Opening a door through telepathic visualisation is from the novelisation of The Doomsday Weapon.
Teeth! Idris is bitey.
Hats! Some pretty good examples on Auntie and Uncle, plus Idris' wig.
Fish! "Like fish fingers!" "Oh, do fish have fingers?" Idris taking the mick.
Small Child! Not a literal one, but the Auntie-Uncle-Nephew setup has a metaphorical one in Nephew.
Item Most Likely to Wind Up as a Toy: Idris, naturally. Though you can already make your own custom Nephew figure by painting the eyes of an Ood figurine with glow-in-the-dark green paint.