The anchor line (rope) gets saturated with water and then retrieved and piled up in the anchor locker. You will have water in the compartment whether rain enters through that door or not. The compartment should be watertight to the rest of the boat.
You might try taping a cover (plastic sheet or ???) over the top deck access door to see if it makes any difference.
If you have the mirror on the front wall of the cabin like my 268, you might try removing it by lifting it straight up about 2 inches. There is an access hatch (at least on my 268) that you can unscrew and remove to get at the anchor locker compartment. It looks like this:
http://www.westmarine.com/buy/barton-ma ... --15770654 With the boat in the water it might be harder to check the drains for the anchor locker. Some others have had a leak in the rear wall of the compartment where it joins the boat hull. You might also check the hatch in the rear wall for leaks. You might make sure you don't have any insects in the anchor locker before opening that hatch.
One tip to try to trace down leaks is to use those light blue paper towels. They change color when they get wet. Placing them in hard to reach places may help trace the source of the leak.