In Kate's trial, Jack testifies that Oceanic 815 "crash landed on an island in the South Pacific." However, in Confirmed Dead (2008) it was revealed that the airplane was found at the bottom of the Sunda Trench off Bali, in the Indian Ocean.
When Kate is talking to Claire at the clothes line, in several of Kate's shots it rains slightly, while in Clair's shot the air is always clear.
In the flash forward, Kate is being tried by a district attorney at a state court in California, despite having committed her major crimes (murder, arson, and fraud) in Kansas. These are all crimes prosecuted at the state rather than federal level and would be tried in the state where they occurred. From what has been shown so far, Kate has committed no crimes in California. Even if her flight from prosecution was a federal crime, it would most likely be prosecuted in the federal court by a federal prosecutor serving Kansas and not by a district attorney in California. Additionally, the more serious charge of murder would take precedence over the more minor federal charge mentioned, assault of a U.S. Marshal.
When Locke throws the plate of eggs against the wall of the basement you can see it wobble, revealing that it is not cement, but merely a stage.