While the new Doctor is picking out his new clothes he briefly considers an item of clothing that looks like it's from the Restoration period (red, blue collar, made of silk). The costume was one of David Tennant's outfits from Casanova (2005), the series he previously worked on with Russell T. Davies.
For the shots where the Sycorax are first shown, they were intentionally posed to resemble Queen: Bohemian Rhapsody (1975).
In the wide shots of the city you can see scaffolding around Big Ben, in the process of being rebuilt after Aliens of London (2005).
David Tennant is credited as "The Doctor", as opposed to Christopher Eccleston who was credited as "Doctor Who". The change in the credit was done at Tennant's request.
A scene where the Tenth Doctor tries to say his old catchphrase ("Fantastic!") and realizes it doesn't sound right anymore was filmed but not included in the final version. It is available as part of the deleted scenes on the DVD.