...Now that I think about it, anybody who opposes him is going to have to be really careful about fighting other gods.
ED: Depending on what we count as murder.
Murder is defined (by Shaq, for the purposes of this) as the killing of one sapient being by another. Beast killing a beast doesn't count. Sapient killing a beast doesn't count (but does come under Hunting, a separate sphere). Beast killing a sapient doesn't count, but is pretty horrifying. Only a sapient killing another sapient counts as murder - and it counts no matter the reason for the kill.
Shaq's memory ability is both a terrible limitation and a potential advantage. He can
only know what murderers/murdered knew at the time of the murder, but he does know
everything they knew. This has been the reason that Shaq hasn't travelled south once since his creation - nobody, or very few, murdered anyone else thanks to the influence of their patron gods.
However, there are two/three ways we can refine Shaq's ability. The first is simply to rule that demigods and gods are completely immune to this - whether they be killer or killed. The second is that there is an order of precedence involved. If a god kills a mortal, either only the mortal's memory transfers or there's just no effect. If a god kills a demigod, quite possibly no effect there either. If a demigod kills a mortal, only the mortal's memory transfers. If a demigod kills a demigod,
both memories transfer (though not powers, unless that power was sheer skill). If a mortal kills a demigod, both transfer. If a demigod kills a god, perhaps just the demi? But gods killing each other, whilst on an equal level, are probably too extensive in terms of experience for Shaq to absorb at once anyway.
I'm not sure. Perhaps Caesar can give a better ruling on this. The simplest is mortals only, a more complex one would be mortals/demigods. God memory absorption is probably ridiculously overpowered.