Headlight and climate control fan staying on...
 

My 2004 X5 seems to have odd electrical issues happening in the last couple days. The auto lights stayed on last night, and then this morning the climate control fan would not shut off even when the car was off and the key removed. I am wondering if the battery might be going. I know my mothers e46 got very weird right before its battery failed. Any experience on these issues?

If what you're talking about with the lights is eht headlights staying on for about an extra 40 seconds after you shut it off, you may have hit the stalk for flash to pass after turning it off which turns on the "home lights" to light up your driveway as youwalk to the door.

For the fan staying on after the key is off I'd say that is one of the classic symptoms of a failing final stage blower resistor. (FSR) That can actually drain your battery overnight so if it stays on pull the blower fuse to prevent that from happening until you change the FSR.