Martha's earpiece disappears in a shot before she uses Project Indigo, and reappears when she says: "Bye, Jack" (and then takes it out).
When the Daleks attack UNIT, Suzanne (Andrea Harris) is shot by a Dalek as she is running away. Problem is is that she jumps like she's been hit half a second before the beam actually hits her.
Harriet Jones redirects the "Subwave" network to Torchwood in Cardiff, but the map shows Swansea which is 50 miles away.
During the scenes where Martha is in New York, you might be able to notice an English style EXIT sign (with a person running towards a door on a green background), yet the scenes are set in the United States, and hence the sign should simply say EXIT.
In "The Stolen Earth", a newscaster with an American accent refers to the UN issuing an "edict", which she pronounces with a short E. Americans pronounce edict with a long E.