I am about to purchase a new LED Clock for the bedroom. One I am interested in has a feature called Auto Dimmer. Basically, it automatically dims the LED display when the room is dark, so as not to disturb ones sleep. Is there any problem buying this product, as I am concerned that closing the bedroom door on Friday night may cause it to dim the display?

I would think it will be permissible just as you are allowed to talk to a hearing aid that will indicate the level of your voice with a LED indicator, this is permissible since you are not switching anything on or connecting ant electric or electronic circuit since it is all on from before. (laws of the sick on Shabbat by the Schlezinger institute)