From the Gene Roddenberry quote in this answer:
'In answering these questions, I came up with the statement that "this time system adjusts for shifts in relative time which occur due to the vessel's speed and space warp capability. It has little relationship to Earth's time as we know it. One hour aboard the U.S.S. Enterprise at different times may equal as little as three Earth hours."'
Hold on a second, is this a reference to relativistic effects? Time dilation? Do ships at warp even experience time dilation? (I'd assumed the special-ness of subspace travel prevented this.) Are there any in-universe references to a crew at warp experiencing a different duration of time than people who are stationary (say, on a planet or in a station)?