Yeah, the omni properties of god that we tend to discuss in Philosophy of Religion are Omniscience, omnipresence, omnipotence, and all good.
They can't all be true, I.E. God cannot do logically impossible things like make a rock so heavy he cannot lift it or make a square circle. But, so what if you can't make or do things that are logically impossible? If God is around and is all good, but not omnipotent, then who cares? He's still the most powerful thing around (if he exists).
Well, that's the way folks in my circle figure it.
Problem with losing omniscience is, he wouldn't be a good judge without it. Don't want God not knowing how good folks were during their lives, or forgetting someone like MLK's life and sacrifices, or not knowing that some scumbag snuck children into his basement and kept them as slaves.. God wouldn't be just then.
Problem with losing omnipresence is, he might die or end.
Folks don't want a God that isn't all good, or he's not worthy of following
So the easiest thing to forgo is omnipotence, since you could give up some power and still be logical, and still be omnipotent in terms of things that exist/ most powerful thing there is by far.
This also brings up some interesting stuff like, thinking about God outside of space and time/ timespace.. Looking at time, existence, everything that ever took place on something like a sheet of paper that he comprehends perfectly (kind of strange to even imagine this, like having a book flayed out and just knowing it). This is some pretty neat stuff to think about, at least to me it used to be