I replaced the dome light with a blue LED. It works fits well, I can turn it off all the way and on. My problem is when I leave it on auto and all of the doors are closed and the car is locked the light is still on. What could be the cause of this?

 

Mine does the same thing. Its because leds draw different than a conventional filament bulb. It goes off eventually or once you start the car. Mine does at least?

 

My courtasy light turn off once the car is started (I assume once the car is locked and some time has passed as well). As far as the dome light goes I think it stays on 24/7 very minimaly though. Once the automatic light turn off it just turns to a very dim output, so dimit you can hardly see it in daytime. I figure I can just leave it on when needed cause it shouldntdrain much power. Also only turn it on auto when goingout after dark.

 

yeah there is about 2v that is always applied to that socket for some reason...i checked it out in mine and thats why

 

LEDs have a very low current draw and therefore are able to utilize that always-on 2V of power to the dome light. Unfortunately this is not optimal in your situation. This is also why replacing standard flasher bulbs with LEDs usually results in a fast flash. The lower resistance and current draw of the LED differs from what the electrical system was designed for which is why you need aftermarket relays or additional resistors.
I'm not sure what the specification of your LED is but try adding a resistor in between the power source and LED. Perhaps a typical 1k resistor, make sure it's rated for 12V.