NASA must be envious. They'd probably pay billions to just set a timer to their space junk and have it poof out of existence in thirty days. The difference between NASA and CCP is that CCP can do something about their junk. According to the EVE Trinity 1.2 patch notes, starting April 16, anchored containers which are not in the vicinity of a starbase and have not been interacted with will be given a thirty day timer. At the end of that, if nobody has touched them, they will just be given a short trip through a wormhole into the Dimension of Unwanted Trash. Further, at the first of every month, abandoned drones, fighters, shuttles and rookie ships will be scrapped as a hazard to navigation. With the trash gone, bookmarks pointing to them will become invalid. To save y our bookmarks that point to junk, go through the list and redirect them to coordinates in space (right-click in space next to the container) instead of some random orbiting piece of space debris. Be sure to do this before Downtime on the 16th, because they will be poofed when EVE comes back up if you have not switched them to coordinates before then.
If your ship takes more time to undock in the morning, it may just be getting old. Or it could just be that in a re-balancing, your ship had fewer equipment slots than it had the night before. You may no longer leave a station until you remove the excess equipment. Along with the Junk In Space initiative, EVE Trinity 1.2 also includes a huge number of UI and game fixes. They even managed to close a few exploits -- and the world is a better place for us all.