Idle drops slightly and interior lights dimming

[duckseatfree]

I have a 2005 x5 4.4i with 109k miles.

My issue is that the car idles normally, then there is a slight drop in the RPMs - you can't really tell by the gauge but I can both hear it and feel a slight vibration change. Also, when this happens I can see the light in the vanity mirror dim, then brighten again (this also happens while I am driving). I recently had the Trans failsafe mode warning (2nd time) on but the battery was bad; I bought a new battery (holding charge well) and the alternator is also doing well.

The first time I had the Trans failsafe mode warning on I was warming up the car a in December (about 12 degress F) and I went inside. A few minutes later I could here the car beeping (not the horn) and the idle was extremely rough. I shut the car off, waited 1 minute and tried to start the car again but the Trans failsafe warning was on so I turned it off. I waited about 10 minutes and restarted and everything was fine.

Could my idle problem be some kind of leak or voltage regulator problem? Or could it be something bigger?