Factual error: To protect the warp core, Janeway instructs Paris to move away from the rings at Warp 7. Moments later (Janeway, Torres and Tuvok are still in the same position), Paris tells Janeway they are 0.6 light years away from the rings. Warp 7 is 656 times the speed of light. It would take about 8 hours to travel 0.6 light years at Warp 7.
Factual error: Chakotay says "if our orbit starts to decay, Voyager will begin to feel the effects of the differential, and we'll begin aging hundreds of times faster than we would in normal space". Whilst it is true that they would be aging faster relative to normal space, they would not instantly become old. Time would simply slow around them, so whilst they would be aging faster relative to normal space, they would not all of a sudden become really old - which is how it is made out to be. They would all age the same amount whether in a standard orbit or in a more decayed orbit. (00:06:37)
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.