I have a DeanML79 and had it recently set up to play twelves. I've broken the strings in and they all stay in tune, with the exception of the low E string.

It will go above and below pitch and becomes so annoying I can't stand it when there is even a hint of distortion. What do I do?

I can't play even power chords with out it going above and below being in tune and not ****ty sounding
When shit hits the fan...step to the side of the fan.
Your 6th string tuning knob sounds like it's ****ed. I'm not sure though.
Only play what you hear. If you don’t hear anything, don’t play anything.
-Chick Corea
Make sure you tune it correctly, and im not so sure but if it's a floating trem i advise locking the nuts at the neck so the strings dont go out of tune and if the tuning problem persists after locking them then mess around with the fine tuners. if you dont have a floating trem then none of the aforementioned advice will help, which basically means ur F**** but it could be what food1010 said ur tuner might be messed up. PM me cuz if u live near me i might be able to giv u a number to a guy whose a guitar tech and has been voted number 1 in the East Coast
It's not the floating trem version
When shit hits the fan...step to the side of the fan.
yeah i saw i checked out muscians friend and saw the main model has to floating trem . ur best bet is what food1010 said a bad tuner