When Martha is comparing the 2 plans side by side, the drawing of the dalek sections in the top right hand corner has vanished.
Three times an old fashioned "knife-blade" switch is opened which would break the circuit (ie the "off" position), but the result is that something is turned on.
When the solar flare is imminent The Doctor orders a Power-up. The knife switches in the following shot are shown being opened - disconnecting them from the electrical contacts - effectively preventing a Power-up.
When the human/Dalek turns over the now-broken radio, the name "Hamilton" appears in mirror-image, indicating that the film stock was reversed.
The Statue of Liberty is shown with the all gold-leaf surface torch that was put in place in 1984. In 1930, the torch was made of glass panes mounted on a copper frame.
In a view from Hooverville, the yet to be finished Empire State Building shows its flood lights on its sides. These flood lights were not added until 1964.
A warning sign in the Empire State Building referring to "the lift" should have used the American English term "the elevator". In addition, Laszlo, an American, also uses the term lift when he should have said elevator.
The Doctor tells the Daleks that "this planet hasn't even split the atom yet". Lord Ernest Rutherford first split the atom in 1917, at least 12 years before the Great Depression and the first Hooverville was established.
Tallulah, a New Yorker, makes a malaprop involving "gammon," a British dish which Americans are unlikely to have heard of.