The Voyager Conspiracy - S6-E9
Factual error: When the alien contacts Voyager after his catapult jump, he states that he is 5,000 light years away. Despite the distance, he and Janeway have a real time conversation. With this incredible communications technology, Voyager (which is at this point less than 55,000 light years from the Alpha Quadrant) should be able to have several back and forth conversations a day with Starfleet.