Battery in my truck is dated Jan 2012. Still starts *almost* every time, unless I've left it sitting for a month in cold weather or something.
I've had batteries last 10 years before. Just depends on what kind of battery you get. A $70 wal-mart special is not going to last as long as some better brands.
But yeah, I had issues with my dome light not working with the door open but randomly coming on while driving down the street so I just pulled the bulbs. Now that you mention it though, it did start acting up after tapping into it to power my "temporary" head unit (that still sits on the passenger seat floor because I refuse to cut my dash). I don't know if they're related though, the dimmer on my headlight switch that also turns the dome light on has always been screwy. Maybe I'll get around to replacing that AND the little door plunger thing and see if it makes a difference.