Turn IS off when mounted on tripod.
The IS system is always looking for movement, if there is none it just starts to spaz out.
The IS systems of all but the oldest lenses sense when the lens is on a tripod, and disable themselves. The supertele lenses go a step further, and activate a secondary IS mode that damps mirror/shutter vibrations.
So, with a supertele you're better off leaving IS on when mounted on a tripod. Do keep in mind that the IS system needs ~0.5 s to stabilize the image – if you just mash the shutter release, that's worse than leaving IS off.
Leaving IS on doesn't affect sharpness, at least based on some limited testing I've done. See this post
, scroll down for results from the 600/4L IS II.
I haven't used live view much with my 600 II, but I do leave IS on when on a tripod, and I don't recall any issues, provided the IS is allowed to operate for a brief period (sometimes there's an initial 'jump' then a 'drift' as it settles).
Question for the OP - which IS mode is set on the lens?