When The Doctor tears the page from the book, he puts it in the basket twice.
The hands on the angel in the graveyard change place depending on whether the shot is from the front or from the back.
Whilst River Song's wrist is gripped by the Angel, the position of the statue's grip changes between shots.
When Rory kisses Amy in the park and says "Coffee," Amy's knee is up, but when the camera changes to a longer shot, both her knees are now flat.
The book is open in the middle when The Doctor tears the page out, so it couldn't be the last page as he claims.
In the first scene, in 1938, the Detective picks up a bundle of money revealing an envelope with an address on it. The address has a ZIP Code on it. Those weren't created until 1963. The ZIP also has the ZIP+4 format which was not started until 1983.
The Statue of Liberty's torch is painted gold in 1938. This renovation was added between 1984 and 1986.
Even though 11 was supposed to be the last incarnation of The Doctor (hence no more regeneration energy to regenerate), he heals River Song's broken wrist using regeneration energy.