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 in Lost, 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.
The courtroom scene contains numerous errors in how proceedings are conducted, ones that are noticeable to those with even a nodding acquaintance with American legal proceedings. Among them are the fact that the prosecution presents its case first and then the defense.
The goof item below may give away important plot points.
In Kate's trial seen in the flash-forward flashback, Jack testifies that Oceanic 815 "crash landed on an island in the South Pacific." While this is true, Jack stating this under oath would be shocking news to the world. The plane planted by Charles Widmore was found at the bottom of a deep trench in the Indian Ocean, near Indonesia, and northwest of Australia. To protect the people still on the island, the Oceanic Six backed up WIdmore's fraudulent plane crash in the Indian Ocean, and that they escaped before it sank and floated for days before washing up on an island. Jack suddenly changing the story and stating that the plane actually crashed on an island in the South Pacific would cause severe confusion at the trial and problems for the Oceanic Six.